Quizbank/Electricity and Magnetism (calculus) Exams/Questions list

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Questions
Taken from calcPhyEMt153290827354 1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=3e$$?
 * a) 5.768E-14 N
 * b) 6.344E-14 N
 * c) 6.979E-14 N
 * d) 7.677E-14 N
 * e) 8.444E-14 N

2) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=3e$$?
 * a) 5.217E+01 degrees
 * b) 5.739E+01 degrees
 * c) 6.313E+01 degrees
 * d) 6.944E+01 degrees
 * e) 7.639E+01 degrees

3) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=1.1 m, b=1.9 m.  The total charge on the rod is 2 nC.
 * a) 1.040E+00 V/m2
 * b) 1.145E+00 V/m2
 * c) 1.259E+00 V/m2
 * d) 1.385E+00 V/m2
 * e) 1.523E+00 V/m2

4) A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?
 * a) 4.608E+09 N/C2
 * b) 5.069E+09 N/C2
 * c) 5.576E+09 N/C2
 * d) 6.134E+09 N/C2
 * e) 6.747E+09 N/C2

5) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=5.9\text{ m}$$ and the surface charge density is $$\sigma=4\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=3.5\text{ m}$$.
 * a) 2.021E+00 V/m2
 * b) 2.224E+00 V/m2
 * c) 2.446E+00 V/m2
 * d) 2.691E+00 V/m2
 * e) 2.960E+00 V/m2

6) A large thin isolated square plate has an area of 9 m2. It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?
 * a) 5.020E+01 N/C
 * b) 5.522E+01 N/C
 * c) 6.074E+01 N/C
 * d) 6.681E+01 N/C
 * e) 7.349E+01 N/C

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=4.4 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 9.0m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 35&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
 * a) 6.445E+01 N&middot;m2/C
 * b) 7.089E+01 N&middot;m2/C
 * c) 7.798E+01 N&middot;m2/C
 * d) 8.578E+01 N&middot;m2/C
 * e) 9.436E+01 N&middot;m2/C

8) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 7.5m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 3.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
 * a) 2.058E+01 N&middot;m2/C
 * b) 2.264E+01 N&middot;m2/C
 * c) 2.491E+01 N&middot;m2/C
 * d) 2.740E+01 N&middot;m2/C
 * e) 3.014E+01 N&middot;m2/C

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.5m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 6.4, 6.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
 * a) 2.662E+01 N&middot;m2/C
 * b) 2.929E+01 N&middot;m2/C
 * c) 3.222E+01 N&middot;m2/C
 * d) 3.544E+01 N&middot;m2/C
 * e) 3.898E+01 N&middot;m2/C

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=6), and (x=4, y=6), where x and y are measured in meters. The electric field is, $$\vec E=3y^{1.9}\hat i +3x^{1.5}\hat j +3y^{1.6}\hat k$$
 * a) 3.658E+02 V&middot;m
 * b) 4.024E+02 V&middot;m
 * c) 4.426E+02 V&middot;m
 * d) 4.869E+02 V&middot;m
 * e) 5.355E+02 V&middot;m

11) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.5 m from the center of the shells?
 * a) 6.171E+00 N/C
 * b) 6.789E+00 N/C
 * c) 7.467E+00 N/C
 * d) 8.214E+00 N/C
 * e) 9.036E+00 N/C

12) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=3 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 1.4 m from the center?
 * a) 1.327E+02 N/C
 * b) 1.460E+02 N/C
 * c) 1.606E+02 N/C
 * d) 1.767E+02 N/C
 * e) 1.943E+02 N/C

13) A 5 C charge is separated from a 9 C charge by distance of 15 cm.  What is the work done by increasing this separation to 21 cm?
 * a) 7.003E-07 J
 * b) 7.704E-07 J
 * c) 8.474E-07 J
 * d) 9.321E-07 J
 * e) 1.025E-06 J

14) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=4 &mu;C, q3=7 &mu;C, and q4=8 &mu;C. How much work was required to assemble these four charges from infinity?
 * a) 2.573E+01 J
 * b) 2.831E+01 J
 * c) 3.114E+01 J
 * d) 3.425E+01 J
 * e) 3.768E+01 J

15) A 12.0 V battery can move 9,000 C of charge. How many Joules does it deliver?
 * a) 8.114E+04 J
 * b) 8.926E+04 J
 * c) 9.818E+04 J
 * d) 1.080E+05 J
 * e) 1.188E+05 J

16) When a 7.85 V battery operates a 1.82 W bulb, how many electrons pass through it each second?
 * a) 1.087E+18 electrons
 * b) 1.196E+18 electrons
 * c) 1.316E+18 electrons
 * d) 1.447E+18 electrons
 * e) 1.592E+18 electrons

17) Calculate the final speed of a free electron accelerated from rest through a potential difference of 3 V.
 * a) 9.339E+05 m/s
 * b) 1.027E+06 m/s
 * c) 1.130E+06 m/s
 * d) 1.243E+06 m/s
 * e) 1.367E+06 m/s

18) An electron gun has parallel plates separated by 2.57 cm and gives electrons 53 keV of energy. What force would the field between the plates exert on a 0.58 &mu;C charge that gets between the plates?
 * a) 9.885E-01 N
 * b) 1.087E+00 N
 * c) 1.196E+00 N
 * d) 1.316E+00 N
 * e) 1.447E+00 N

19) Assume that a 21 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (5 cm, 0&deg;) and  P2 is at (16 cm, 51&deg;).
 * a) 2.145E+03 V
 * b) 2.359E+03 V
 * c) 2.595E+03 V
 * d) 2.855E+03 V
 * e) 3.140E+03 V

20) A Van de Graff generator has a 81 cm diameter metal sphere that produces 235 kV near its surface. What  is the excess charge on the sphere?
 * a) 9.627E+00 &mu;C
 * b) 1.059E+01 &mu;C
 * c) 1.165E+01 &mu;C
 * d) 1.281E+01 &mu;C
 * e) 1.409E+01 &mu;C

21) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.25 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.12 cm)? Note that following the textbook's example, the y-value of the field point at 2.12 cm matches the disance of the positive charge above the x-axis.
 * a) 6.901E+02 V
 * b) 7.591E+02 V
 * c) 8.350E+02 V
 * d) 9.185E+02 V
 * e) 1.010E+03 V

22) If a 22 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=16 V is x2 + y2 + z2 = R2, where R=
 * a) 8.441E+00 m
 * b) 9.285E+00 m
 * c) 1.021E+01 m
 * d) 1.123E+01 m
 * e) 1.236E+01 m

23) Two large parallel conducting plates are separated by 7.57 mm. Equal and opposite surface charges of 7.830E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 57 V?
 * a) 6.446E-01 mm
 * b) 7.412E-01 mm
 * c) 8.524E-01 mm
 * d) 9.803E-01 mm
 * e) 1.127E+00 mm

24) An empty parallel-plate capacitor with metal plates has an area of 1.89 m2, separated by 1.36 mm. How much charge does it store if the voltage is 4.040E+03 V?
 * a) 3.395E+01 &mu;C
 * b) 3.735E+01 &mu;C
 * c) 4.108E+01 &mu;C
 * d) 4.519E+01 &mu;C
 * e) 4.971E+01 &mu;C

25) What is the net capacitance if C1=4.41 &mu;F, C2=4.54 &mu;F, and C3=2.91 &mu;F in the configuration shown?
 * a) 3.515E+00 &mu;F
 * b) 3.867E+00 &mu;F
 * c) 4.254E+00 &mu;F
 * d) 4.679E+00 &mu;F
 * e) 5.147E+00 &mu;F

26) In the figure shown C1=17.6 &mu;F, C2=2.19 &mu;F, and C3=5.84 &mu;F. The voltage source provides &epsilon;=5.4 V. What is the charge on C1?
 * a) 2.707E+01 &mu;C
 * b) 2.978E+01 &mu;C
 * c) 3.275E+01 &mu;C
 * d) 3.603E+01 &mu;C
 * e) 3.963E+01 &mu;C

27) In the figure shown C1=15.5 &mu;F, C2=2.72 &mu;F, and C3=5.1 &mu;F. The voltage source provides &epsilon;=5.89 V. What is the energy stored in C2?
 * a) 8.800E+00 &mu;J
 * b) 9.680E+00 &mu;J
 * c) 1.065E+01 &mu;J
 * d) 1.171E+01 &mu;J
 * e) 1.288E+01 &mu;J

28) What is the average current involved when a truck battery sets in motion 702 C of charge in 2.92 s while starting an engine?
 * a) 2.404E+02 A
 * b) 2.645E+02 A
 * c) 2.909E+02 A
 * d) 3.200E+02 A
 * e) 3.520E+02 A

29) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=38 C  and $$\tau=$$0.0106 s. What is the current at $$t=$$0.0123 s?
 * a) 1.021E+03 A
 * b) 1.123E+03 A
 * c) 1.236E+03 A
 * d) 1.359E+03 A
 * e) 1.495E+03 A

30) Calculate the drift speed of electrons in a copper wire with a diameter of 3.32 mm carrying a 18.4 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.
 * a) 1.195E-04 m/s
 * b) 1.315E-04 m/s
 * c) 1.446E-04 m/s
 * d) 1.591E-04 m/s
 * e) 1.750E-04 m/s

31) A make-believe metal has a density of 5.880E+03 kg/m3 and an atomic mass of 73.2 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.
 * a) 4.396E+28 e&minus;/m3
 * b) 4.836E+28 e&minus;/m3
 * c) 5.319E+28 e&minus;/m3
 * d) 5.851E+28 e&minus;/m3
 * e) 6.436E+28 e&minus;/m3

32) A device requires consumes 121 W of power and requires 5.12 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.
 * a) 8.849E+05 A/m2
 * b) 9.734E+05 A/m2
 * c) 1.071E+06 A/m2
 * d) 1.178E+06 A/m2
 * e) 1.296E+06 A/m2

33) Calculate the resistance of a 12-gauge copper wire that is 97 m long and carries a current of 29 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.
 * a) 4.923E-01 &Omega;
 * b) 5.416E-01 &Omega;
 * c) 5.957E-01 &Omega;
 * d) 6.553E-01 &Omega;
 * e) 7.208E-01 &Omega;

34) Calculate the electric field in a 12-gauge copper wire that is 75 m long and carries a current of 21 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.
 * a) 7.280E-05 V/m
 * b) 8.008E-05 V/m
 * c) 8.809E-05 V/m
 * d) 9.690E-05 V/m
 * e) 1.066E-04 V/m

35) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.14 &Omega; at a temperature of 77&deg;C and that the temperature coefficient of expansion is 4.750E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 542 &deg;C?
 * a) 6.540E+00 &Omega;
 * b) 6.867E+00 &Omega;
 * c) 7.210E+00 &Omega;
 * d) 7.571E+00 &Omega;
 * e) 7.949E+00 &Omega;

36) A DC winch moter draws 31 amps at 191 volts as it lifts a 5.080E+03 N weight at a constant speed of 0.99 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.
 * a) 6.972E-01 &Omega;
 * b) 7.669E-01 &Omega;
 * c) 8.436E-01 &Omega;
 * d) 9.280E-01 &Omega;
 * e) 1.021E+00 &Omega;

37) What is consumer cost to operate one 77&minus;W incandescent bulb for 12 hours per day for 1 year (365 days) if the cost of electricity is $0.134 per kilowatt-hour?
 * a) $3.087E+01
 * b) $3.395E+01
 * c) $3.735E+01
 * d) $4.108E+01
 * e) $4.519E+01

38) A given battery has a 12 V emf and an internal resistance of 0.193 &Omega;. If it is connected to a 0.89 &Omega; resistor what is the power dissipated by that load?
 * a) 8.210E+01 W
 * b) 9.030E+01 W
 * c) 9.934E+01 W
 * d) 1.093E+02 W
 * e) 1.202E+02 W

39) A battery with a terminal voltage of 14.9 V is connected to a circuit consisting of 2 23.3 &Omega; resistors and one 13.6 &Omega; resistor. What is the voltage drop across the 13.6 &Omega; resistor?
 * a) 3.366E+00 V
 * b) 3.703E+00 V
 * c) 4.073E+00 V
 * d) 4.480E+00 V
 * e) 4.928E+00 V

40) Three resistors, R1 = 1.7 &Omega;, and R2 = R2 = 3.75 &Omega;, are connected in parallel to a 9.74 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)
 * a) 4.193E+01 W
 * b) 4.612E+01 W
 * c) 5.073E+01 W
 * d) 5.580E+01 W
 * e) 6.138E+01 W

41) In the circuit shown V=19.9 V, R1=1.69 &Omega;, R2=7.02 &Omega;, and R3=12.8 &Omega;. What is the power dissipated by R2?
 * a) 2.993E+01 W
 * b) 3.293E+01 W
 * c) 3.622E+01 W
 * d) 3.984E+01 W
 * e) 4.383E+01 W

42) The resistances in the figure shown are R1= 1.35 &Omega;, R2= 1.52 &Omega;, and R2= 2.45 &Omega;. V1 and V3 are text 0.419 V and 2.37 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.511 V. What is the absolute value of the current through R1?
 * a) 8.841E-02 A
 * b) 9.725E-02 A
 * c) 1.070E-01 A
 * d) 1.177E-01 A
 * e) 1.294E-01 A

43) Two sources of emf &epsilon;1=52.2 V, and  &epsilon;2=15.4 V are oriented as shownin the circuit. The resistances are R1=4.89 k&Omega; and  R2=2.76 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.99 mA and I4=0.693 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?
 * a) 1.726E+00 mA
 * b) 1.898E+00 mA
 * c) 2.088E+00 mA
 * d) 2.297E+00 mA
 * e) 2.527E+00 mA

44) Two sources of emf &epsilon;1=57.8 V, and  &epsilon;2=18.5 V are oriented as shownin the circuit. The resistances are R1=2.53 k&Omega; and  R2=1.8 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=7.15 mA and I4=1.27 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?
 * a) 1.276E+01 V
 * b) 1.404E+01 V
 * c) 1.544E+01 V
 * d) 1.699E+01 V
 * e) 1.869E+01 V

45) Two sources of emf &epsilon;1=60.7 V, and  &epsilon;2=16.7 V are oriented as shownin the circuit. The resistances are R1=4.72 k&Omega; and  R2=2.33 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.65 mA and I4=0.946 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?
 * a) 1.981E+01 V
 * b) 2.180E+01 V
 * c) 2.398E+01 V
 * d) 2.637E+01 V
 * e) 2.901E+01 V

46) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 379 V.  If the combined external and internal resistance is 158 &Omega and the capacitance is  95 mF, how long will it take for the capacitor's voltage to reach 234.0 V?
 * a) 1.084E+01 s
 * b) 1.192E+01 s
 * c) 1.311E+01 s
 * d) 1.442E+01 s
 * e) 1.586E+01 s

47) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 5.11 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (8.99 i + 7.56 j  + 8.49 k) x 104 m/s?
 * a) 1.124E-13 N
 * b) 1.236E-13 N
 * c) 1.360E-13 N
 * d) 1.496E-13 N
 * e) 1.645E-13 N

48) A charged particle in a magnetic field of 2.780E-04 T is moving perpendicular to the magnetic field with a speed of 6.370E+05 m/s. What is the period of orbit if orbital radius is 0.671 m?
 * a) 6.017E-06 s
 * b) 6.619E-06 s
 * c) 7.280E-06 s
 * d) 8.008E-06 s
 * e) 8.809E-06 s

49) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0783 T . It emerges after being deflected by 64&deg; from its original direction. How much time did it spend in that magnetic field?
 * a) 2.224E-07 s
 * b) 2.446E-07 s
 * c) 2.691E-07 s
 * d) 2.960E-07 s
 * e) 3.256E-07 s

50) A 18 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.351 T. What current is required to maintain this balance?
 * a) 1.241E+00 A
 * b) 1.365E+00 A
 * c) 1.501E+00 A
 * d) 1.652E+00 A
 * e) 1.817E+00 A

51) A long rigind wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.899 T magnetic field is directed 43&deg; away from the wire?
 * a) 3.685E+00 N/m
 * b) 4.054E+00 N/m
 * c) 4.459E+00 N/m
 * d) 4.905E+00 N/m
 * e) 5.395E+00 N/m

52) A circular current loop of radius 2.86 cm carries a current of 1.7 mA. What is the magnitude of the torque if the dipole is oriented at 43 &deg; to a uniform magnetic fied of 0.729 T?
 * a) 1.483E-06 N m
 * b) 1.632E-06 N m
 * c) 1.795E-06 N m
 * d) 1.974E-06 N m
 * e) 2.172E-06 N m

53) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 5.53 mT and 7.210E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?
 * a) 8.905E+05 m/s
 * b) 9.796E+05 m/s
 * c) 1.078E+06 m/s
 * d) 1.185E+06 m/s
 * e) 1.304E+06 m/s

54) The silver ribbon shown are a=4.65 cm, b=3.92 cm, and c= 1.23 cm. The current carries a current of 89 A and it lies in a uniform magnetic field of 2.4 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
 * a) 1.255E-06 V
 * b) 1.380E-06 V
 * c) 1.518E-06 V
 * d) 1.670E-06 V
 * e) 1.837E-06 V

55) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.398 m and a magneticfield of 0.855 T. What is their maximum kinetic energy?
 * a) 5.581E+00 MeV
 * b) 6.139E+00 MeV
 * c) 6.753E+00 MeV
 * d) 7.428E+00 MeV
 * e) 8.171E+00 MeV

56) A wire carries a current of 316 A in a circular arc with radius 1.55 cm swept through 76 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?
 * a) 8.070E+00 Tesla
 * b) 8.878E+00 Tesla
 * c) 9.765E+00 Tesla
 * d) 1.074E+01 Tesla
 * e) 1.182E+01 Tesla

57) Three wires sit at the corners of a square of length 0.811 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.18 A, 1.44 A, 1.46 A), respectively. What is the x-component of the magnetic field at point P?
 * a) Bx= 4.887E-05 T
 * b) Bx= 5.376E-05 T
 * c) Bx= 5.914E-05 T
 * d) Bx= 6.505E-05 T
 * e) Bx= 7.156E-05 T

58) Three wires sit at the corners of a square of length 0.762 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.69 A, 1.7 A, 1.02 A), respectively. What is the y-component of the magnetic field at point P?
 * a) By= 5.510E-05 T
 * b) By= 6.061E-05 T
 * c) By= 6.667E-05 T
 * d) By= 7.333E-05 T
 * e) By= 8.067E-05 T

59) Two parallel wires each carry a 5.0 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.48 cm, 0.973 cm), while the other is located at (3.32 cm, 4.79 cm). What is the force per unit length between the wires?
 * a) 1.139E-10 N/m
 * b) 1.253E-10 N/m
 * c) 1.379E-10 N/m
 * d) 1.517E-10 N/m
 * e) 1.668E-10 N/m

60) Two loops of wire carry the same current of 62 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.584 m while the other has a radius of 1.38 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.341 m from the first (smaller) loopif the disance between the loops is 1.21 m?
 * a) 4.102E-02 T
 * b) 4.513E-02 T
 * c) 4.964E-02 T
 * d) 5.460E-02 T
 * e) 6.006E-02 T

61) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.34 mm from the center of a wire of radius 3 mm if the current is 1A?
 * a) 2.237E-05 T
 * b) 2.461E-05 T
 * c) 2.707E-05 T
 * d) 2.978E-05 T
 * e) 3.276E-05 T

62) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.703 m and $$B_{max}=\,$$ 0.521 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.165 m that is centered on the axis with its plane perpendicular to the axis?
 * a) 1.338E+05 A
 * b) 1.472E+05 A
 * c) 1.619E+05 A
 * d) 1.781E+05 A
 * e) 1.959E+05 A

63) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.39 kA, I2=2.19 kA, and I3=3.68 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:
 * a) 1.547E-03 T-m
 * b) 1.702E-03 T-m
 * c) 1.872E-03 T-m
 * d) 2.060E-03 T-m
 * e) 2.266E-03 T-m

64) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.37 kA, I2=1.05 kA, and I3=2.99 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:
 * a) 4.069E-03 T-m
 * b) 4.476E-03 T-m
 * c) 4.924E-03 T-m
 * d) 5.416E-03 T-m
 * e) 5.958E-03 T-m

65) A solenoid has 8.230E+04 turns wound around a cylinder of diameter 1.5 cm and length 18 m. The current through the coils is 0.633 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;3.74 cm to z=+3.23 cm
 * a) 1.731E-04 T-m
 * b) 1.905E-04 T-m
 * c) 2.095E-04 T-m
 * d) 2.305E-04 T-m
 * e) 2.535E-04 T-m

66) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 598 mA, the net magnetic field is measured to be 1.38 T. What is the magnetic susceptibility for this case?
 * a) $$\chi \text{ (chi) }=$$ 8.338E+02
 * b) $$\chi \text{ (chi) }=$$ 9.172E+02
 * c) $$\chi \text{ (chi) }=$$ 1.009E+03
 * d) $$\chi \text{ (chi) }=$$ 1.110E+03
 * e) $$\chi \text{ (chi) }=$$ 1.221E+03

67) A square coil has sides that are L= 0.673 m long and is tightly wound with N=211 turns of wire. The resistance of the coil is R=5.31 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0454 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
 * a) 6.753E-01 A
 * b) 7.428E-01 A
 * c) 8.171E-01 A
 * d) 8.988E-01 A
 * e) 9.887E-01 A

68) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.317 m. The magnetic field is spatially uniform but decays in time according to $$(3.5)e^{-\alpha t}$$, where $$\alpha=$$6.25 s. What is the current in the coil if the impedance of the coil is 52.3 &Omega;?
 * a) 6.717E-02 A
 * b) 7.388E-02 A
 * c) 8.127E-02 A
 * d) 8.940E-02 A
 * e) 9.834E-02 A

69) The current through the windings of a solenoid with n= 2.120E+03 turns per meter is changing at a rate dI/dt=4 A/s. The solenoid is 94 cm long and has a cross-sectional diameter of 2.56 cm.  A small coil consisting of N=30turns wraped in a circle of diameter 1.15 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
 * a) 3.019E-05 V
 * b) 3.321E-05 V
 * c) 3.653E-05 V
 * d) 4.018E-05 V
 * e) 4.420E-05 V

70) Calculate the motional emf induced along a 40.1 km conductor moving at an orbital speed of 7.85 km/s perpendicular to Earth's 5.160E-05 Tesla magnetic field.
 * a) 1.477E+04 V
 * b) 1.624E+04 V
 * c) 1.787E+04 V
 * d) 1.965E+04 V
 * e) 2.162E+04 V

71) A cylinder of height 1.98 cm and radius 2.62 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.33 cm from point O and moves at a speed of 2.0 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)
 * a) 6.980E+00 cm3/s
 * b) 7.678E+00 cm3/s
 * c) 8.446E+00 cm3/s
 * d) 9.290E+00 cm3/s
 * e) 1.022E+01 cm3/s

72) A recangular coil with an area of 0.371 m2 and 20 turns is placed in a uniform magnetic field of 2.51 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.060E+03 s&minus;1.  What is the magnitude (absolute value) of the induced emf at t = 88 s?
 * a) 5.694E+04 V
 * b) 6.263E+04 V
 * c) 6.889E+04 V
 * d) 7.578E+04 V
 * e) 8.336E+04 V

73) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.26 T and $$\omega=$$9.250E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.385 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.
 * a) 6.029E+04 V
 * b) 6.631E+04 V
 * c) 7.295E+04 V
 * d) 8.024E+04 V
 * e) 8.826E+04 V

74) A long solenoid has a radius of 0.442 m and 63 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$22 s&minus;1.What is the induced electric fied at a distance 1.94 m from the axis at time t=0.0331 s ?
 * a) 2.964E-04 V/m
 * b) 3.260E-04 V/m
 * c) 3.586E-04 V/m
 * d) 3.945E-04 V/m
 * e) 4.339E-04 V/m

75) A long solenoid has a radius of 0.508 m and 90 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$25 s&minus;1.What is the induced electric fied at a distance 0.145 m from the axis at time t=0.0643 s ?
 * a) 2.614E-04 V/m
 * b) 2.875E-04 V/m
 * c) 3.163E-04 V/m
 * d) 3.479E-04 V/m
 * e) 3.827E-04 V/m

76) A long solenoid has a length 0.714 meters, radius 4.95 cm, and 578 turns. It surrounds  coil of radius 8.72 meters and 16turns.  If the current in the solenoid is changing at a rate of 248 A/s, what is the emf induced in the surounding coil?
 * a) 6.667E-02 V
 * b) 7.334E-02 V
 * c) 8.067E-02 V
 * d) 8.874E-02 V
 * e) 9.762E-02 V

77) An induced emf of 4.82V is measured across a coil of 73 closely wound turns while the current throuth it increases uniformly from 0.0 to 4.61A in 0.934s. What is the self-inductance of the coil?
 * a) 7.337E-01 H
 * b) 8.071E-01 H
 * c) 8.878E-01 H
 * d) 9.765E-01 H
 * e) 1.074E+00 H

78) A washer has an inner diameter of 2.57 cm and an outer diamter of 4.14 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.33mm$$, and $$n=2.42$$. What is the volume of the washer?
 * a) 7.226E-01 cm3
 * b) 7.949E-01 cm3
 * c) 8.744E-01 cm3
 * d) 9.618E-01 cm3
 * e) 1.058E+00 cm3

79) Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.98 s if &epsilon; = 5.75 V, R = 8.07 &Omega;, and L = 2.84 H?
 * a) 4.109E-01 V
 * b) 4.930E-01 V
 * c) 5.917E-01 V
 * d) 7.100E-01 V
 * e) 8.520E-01 V

80) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.79% of its maximum value if &epsilon; = 8.03 V, R = 2.4 &Omega;, and L = 1.72 H?
 * a) -1.442E+00 s
 * b) -1.586E+00 s
 * c) -1.744E+00 s
 * d) -1.919E+00 s
 * e) -2.111E+00 s

81) In an LC circuit, the self-inductance is 0.0134 H and the capacitance is 3.280E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 5.930E-05 C. How long does it take for the capacitor to become completely discharged?
 * a) 2.722E-04 s
 * b) 2.994E-04 s
 * c) 3.293E-04 s
 * d) 3.622E-04 s
 * e) 3.985E-04 s

82) An ac generator produces an emf of amplitude 78 V at a frequency of 45 Hz. What is the maximum amplitude of the current if the generator is connected to a  60 mF inductor?
 * a) 3.140E+00 A
 * b) 3.454E+00 A
 * c) 3.800E+00 A
 * d) 4.180E+00 A
 * e) 4.598E+00 A

83) An ac generator produces an emf of amplitude 64 V at a frequency of 95 Hz. What is the maximum amplitude of the current if the generator is connected to a  99 mF capacitor?
 * a) 3.126E+00 A
 * b) 3.438E+00 A
 * c) 3.782E+00 A
 * d) 4.160E+00 A
 * e) 4.576E+00 A

84) The output of an ac generator connected to an RLC series combination has a frequency of 510 Hz and an amplitude of 0.69 V;. If R =4 &Omega;, L= 4.30E-03H, and C=9.20E-04 F, what is the impedance?
 * a) 1.054E+01 &Omega;
 * b) 1.159E+01 &Omega;
 * c) 1.275E+01 &Omega;
 * d) 1.402E+01 &Omega;
 * e) 1.542E+01 &Omega;

85) The output of an ac generator connected to an RLC series combination has a frequency of 480 Hz and an amplitude of 0.17 V;. If R =5 &Omega;, L= 6.70E-03H, and C=6.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?
 * a) 1.322E+00 &rad;
 * b) 1.454E+00 &rad;
 * c) 1.600E+00 &rad;
 * d) 1.760E+00 &rad;
 * e) 1.936E+00 &rad;

86) The output of an ac generator connected to an RLC series combination has a frequency of 8.20E+04 Hz and an amplitude of 4 V. If R =5 &Omega;, L= 5.40E-03H, and C=9.80E-06 F, what is the rms power transferred to the resistor?
 * a) 1.865E-04 Watts
 * b) 2.051E-04 Watts
 * c) 2.256E-04 Watts
 * d) 2.482E-04 Watts
 * e) 2.730E-04 Watts

87) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.38 V. The resistance, inductance, and capacitance are R =7 &Omega;, L= 4.10E-03H, and C=7.40E-04 F, respectively. What is the amplitude of the current?
 * a) 4.486E-02 A
 * b) 4.935E-02 A
 * c) 5.429E-02 A
 * d) 5.971E-02 A
 * e) 6.569E-02 A

88) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=1 V. The resistance, inductance, and capacitance are R =0.21 &Omega;, L= 4.80E-03H, and C=3.60E-06 F, respectively.
 * a) Q = 1.739E+02
 * b) Q = 2.000E+02
 * c) Q = 2.300E+02
 * d) Q = 2.645E+02
 * e) Q = 3.041E+02

89) A step-down transformer steps 19 kV down to 220 V. The high-voltage input is provided by a 250 &Omega; power line that carries 4 A of currentWhat is the output current (at the 220 V side ?)
 * a) 2.595E+02 A
 * b) 2.855E+02 A
 * c) 3.140E+02 A
 * d) 3.455E+02 A
 * e) 3.800E+02 A

90) A parallel plate capacitor with a capicatnce C=5.40E-06 F whose plates have an area A=3.50E+03 m2 and separation d=5.70E-03 m is connected via a swith to a 92 &Omega; resistor and a battery of voltage V0=52 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.40E-03?
 * a) 3.876E+01 V
 * b) 4.263E+01 V
 * c) 4.690E+01 V
 * d) 5.159E+01 V
 * e) 5.674E+01 V

91) A parallel plate capacitor with a capicatnce C=1.10E-06 F whose plates have an area A=930.0 m2 and separation d=7.50E-03 m is connected via a swith to a 83 &Omega; resistor and a battery of voltage V0=42 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=3.80E-04?
 * a) 3.765E+03 V/m
 * b) 4.142E+03 V/m
 * c) 4.556E+03 V/m
 * d) 5.012E+03 V/m
 * e) 5.513E+03 V/m

92) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=1.80E+03 m2 and separation d=4.30E-03 m is connected via a swith to a 41 &Omega; resistor and a battery of voltage V0=39 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.60E-04?
 * a) 7.089E-02 A
 * b) 7.798E-02 A
 * c) 8.578E-02 A
 * d) 9.436E-02 A
 * e) 1.038E-01 A

93) A 46 kW radio transmitter on Earth sends it signal to a satellite 140 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?
 * a) 1.764E+02 km
 * b) 1.940E+02 km
 * c) 2.134E+02 km
 * d) 2.347E+02 km
 * e) 2.582E+02 km

94) What is the radiation pressure on an object that is 5.90E+11 m away from the sun and has cross-sectional area of 0.014 m2? The average power output of the Sun is 3.80E+26 W.
 * a) 5.268E-07 N/m2
 * b) 5.795E-07 N/m2
 * c) 6.375E-07 N/m2
 * d) 7.012E-07 N/m2
 * e) 7.713E-07 N/m2

95) What is the radiation force on an object that is 5.20E+11 m away from the sun and has cross-sectional area of 0.04 m2? The average power output of the Sun is 3.80E+26 W.
 * a) 2.242E-08 N
 * b) 2.466E-08 N
 * c) 2.713E-08 N
 * d) 2.984E-08 N
 * e) 3.283E-08 N

Answer Key
1) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=2\times 10^{-7}\text{m}$$. What is the magnitude of the net force on $$q_2$$ if $$q_1=1e$$, $$q_2=-8e$$, and $$q_3=3e$$?
 * + 5.768E-14 N
 * - 6.344E-14 N
 * - 6.979E-14 N
 * - 7.677E-14 N
 * - 8.444E-14 N

2) Three small charged objects are placed as shown, where $$b=2a$$, and $$a=4\times 10^{-7}\text{m}$$.what angle does the force on $$q_2$$ make above the $$-x$$ axis if $$q_1=2e$$, $$q_2=-7e$$, and $$q_3=3e$$?
 * - 5.217E+01 degrees
 * - 5.739E+01 degrees
 * - 6.313E+01 degrees
 * + 6.944E+01 degrees
 * - 7.639E+01 degrees

3) $$E_z(x=0,z)=\int_{-a}^b f(x,z)dx$$ is an integral that calculates the z-component of the electric field at point P situated above the x-axis where a charged rod of length (a+b) is located. The distance between point P and the x-axis is z=1.8 m.  Evaluate $$f(x,y)$$ at x=0.83 m if a=1.1 m, b=1.9 m.  The total charge on the rod is 2 nC.
 * - 1.040E+00 V/m2
 * - 1.145E+00 V/m2
 * - 1.259E+00 V/m2
 * + 1.385E+00 V/m2
 * - 1.523E+00 V/m2

4) A ring is uniformly charged with a net charge of 3 nC. The radius of the ring is R=1.5 m, with its center at the origin and oriented normal to the z axis as shown. what is the magnitude of the electric field at a distance z=1.1 m (on axis) away from the loop's center?
 * + 4.608E+09 N/C2
 * - 5.069E+09 N/C2
 * - 5.576E+09 N/C2
 * - 6.134E+09 N/C2
 * - 6.747E+09 N/C2

5) $$E(z)=\int_{0}^R f(r',z)dr'$$ is an integral that calculates the magnitude of the electric field at a distance $$z$$ fromthe center of a thin circular disk as measured along a line normal to the plane of the disk.  The disk's radius is $$R=5.9\text{ m}$$ and the surface charge density is $$\sigma=4\text{ nC/m}^3$$. Evaluate $$f(r',z)$$ at $$r'=3.5\text{ m}$$.
 * - 2.021E+00 V/m2
 * - 2.224E+00 V/m2
 * - 2.446E+00 V/m2
 * + 2.691E+00 V/m2
 * - 2.960E+00 V/m2

6) A large thin isolated square plate has an area of 9 m2. It is uniformly charged with 8 nC of charge. What is the magnitude of the electric field 3 mm from the center of the plate's surface?
 * + 5.020E+01 N/C
 * - 5.522E+01 N/C
 * - 6.074E+01 N/C
 * - 6.681E+01 N/C
 * - 7.349E+01 N/C

7) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=2.8 m. The other four surfaces are rectangles in y=y0=1.2 m, y=y1=4.4 m, z=z0=1.2 m, and z=z1=4.6 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 9.0m2 ,and those in the zx plane have area 9.5m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 35&deg; above the xy-plane (i.e. above the y axis.) What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
 * - 6.445E+01 N&middot;m2/C
 * - 7.089E+01 N&middot;m2/C
 * - 7.798E+01 N&middot;m2/C
 * + 8.578E+01 N&middot;m2/C
 * - 9.436E+01 N&middot;m2/C

8) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.2 m. The other four surfaces are rectangles in y=y0=1.8 m, y=y1=4.8 m, z=z0=1.8 m, and z=z1=4.3 m. The surfaces in the yz plane each have area 7.5m2. Those in the xy plane have area 3.6m2 ,and those in the zx plane have area 3.0m2. An electric field of magnitude 11 N/C has components in the y and z directions and is directed at 49&deg; from the z-axis. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
 * - 2.058E+01 N&middot;m2/C
 * - 2.264E+01 N&middot;m2/C
 * + 2.491E+01 N&middot;m2/C
 * - 2.740E+01 N&middot;m2/C
 * - 3.014E+01 N&middot;m2/C

9) Each surface of the rectangular box shown is aligned with the xyz coordinate system. Two surfaces occupy identical rectangles in the planes x=0 and x=x1=1.3 m. The other four surfaces are rectangles in y=y0=1.5 m, y=y1=5.0 m, z=z0=1.6 m, and z=z1=4.8 m. The surfaces in the yz plane each have area 11.0m2. Those in the xy plane have area 4.5m2 ,and those in the zx plane have area 4.2m2. An electric field has the xyz components (0, 6.4, 6.8) N/C. What is the magnitude (absolute value) of the electric flux through a surface aligned parallel to the xz plane?
 * + 2.662E+01 N&middot;m2/C
 * - 2.929E+01 N&middot;m2/C
 * - 3.222E+01 N&middot;m2/C
 * - 3.544E+01 N&middot;m2/C
 * - 3.898E+01 N&middot;m2/C

10) What is the magnetude (absolute value) of the electric flux through a rectangle that occupies the z=0 plane with corners at (x,y)= (x=0, y=0), (x=4, y=0), (x=0, y=6), and (x=4, y=6), where x and y are measured in meters. The electric field is, $$\vec E=3y^{1.9}\hat i +3x^{1.5}\hat j +3y^{1.6}\hat k$$
 * - 3.658E+02 V&middot;m
 * - 4.024E+02 V&middot;m
 * - 4.426E+02 V&middot;m
 * + 4.869E+02 V&middot;m
 * - 5.355E+02 V&middot;m

11) Five concentric spherical shells have radius of exactly (1m, 2m, 3m, 4m, 5m).Each is uniformly charged with 2.8 nano-Coulombs. What is the magnitude of the electric field at a distance of 3.5 m from the center of the shells?
 * + 6.171E+00 N/C
 * - 6.789E+00 N/C
 * - 7.467E+00 N/C
 * - 8.214E+00 N/C
 * - 9.036E+00 N/C

12) A non-conducting sphere of radius R=1.7 m has a non-uniform charge density that varies with the distnce from its center as given by &rho;(r)=ar1.6 (r&le;R) where a=3 nC&middot;m-1.4. What is the magnitude of the electric field at a distance of 1.4 m from the center?
 * - 1.327E+02 N/C
 * - 1.460E+02 N/C
 * - 1.606E+02 N/C
 * + 1.767E+02 N/C
 * - 1.943E+02 N/C

13) A 5 C charge is separated from a 9 C charge by distance of 15 cm.  What is the work done by increasing this separation to 21 cm?
 * - 7.003E-07 J
 * + 7.704E-07 J
 * - 8.474E-07 J
 * - 9.321E-07 J
 * - 1.025E-06 J

14) Four charges lie at the corners of a 5 cm by 5 cm square as shown (i.e., a=b=5 cm.)  The charges are q1=3 &mu;C, q2=4 &mu;C, q3=7 &mu;C, and q4=8 &mu;C. How much work was required to assemble these four charges from infinity?
 * - 2.573E+01 J
 * + 2.831E+01 J
 * - 3.114E+01 J
 * - 3.425E+01 J
 * - 3.768E+01 J

15) A 12.0 V battery can move 9,000 C of charge. How many Joules does it deliver?
 * - 8.114E+04 J
 * - 8.926E+04 J
 * - 9.818E+04 J
 * + 1.080E+05 J
 * - 1.188E+05 J

16) When a 7.85 V battery operates a 1.82 W bulb, how many electrons pass through it each second?
 * - 1.087E+18 electrons
 * - 1.196E+18 electrons
 * - 1.316E+18 electrons
 * + 1.447E+18 electrons
 * - 1.592E+18 electrons

17) Calculate the final speed of a free electron accelerated from rest through a potential difference of 3 V.
 * - 9.339E+05 m/s
 * + 1.027E+06 m/s
 * - 1.130E+06 m/s
 * - 1.243E+06 m/s
 * - 1.367E+06 m/s

18) An electron gun has parallel plates separated by 2.57 cm and gives electrons 53 keV of energy. What force would the field between the plates exert on a 0.58 &mu;C charge that gets between the plates?
 * - 9.885E-01 N
 * - 1.087E+00 N
 * + 1.196E+00 N
 * - 1.316E+00 N
 * - 1.447E+00 N

19) Assume that a 21 nC charge is situated at the origin. Calculate the the magnitude (absolute value) of the potential difference between points P1 and  P2 where the polar coordinates (r,&phi;) of  P1 are  (5 cm, 0&deg;) and  P2 is at (16 cm, 51&deg;).
 * - 2.145E+03 V
 * - 2.359E+03 V
 * + 2.595E+03 V
 * - 2.855E+03 V
 * - 3.140E+03 V

20) A Van de Graff generator has a 81 cm diameter metal sphere that produces 235 kV near its surface. What  is the excess charge on the sphere?
 * - 9.627E+00 &mu;C
 * + 1.059E+01 &mu;C
 * - 1.165E+01 &mu;C
 * - 1.281E+01 &mu;C
 * - 1.409E+01 &mu;C

21) A diploe has a charge magnitude of q=9 nC and a separation distance of d=4.25 cm. The dipole is centered at the origin and points in the y-direction as shown. What is the electric potential at the point (x=3.51 cm, y=2.12 cm)? Note that following the textbook's example, the y-value of the field point at 2.12 cm matches the disance of the positive charge above the x-axis.
 * - 6.901E+02 V
 * - 7.591E+02 V
 * + 8.350E+02 V
 * - 9.185E+02 V
 * - 1.010E+03 V

22) If a 22 nC charge is situated at the origin, the equipotential surface for V(x,y,z)=16 V is x2 + y2 + z2 = R2, where R=
 * - 8.441E+00 m
 * - 9.285E+00 m
 * - 1.021E+01 m
 * - 1.123E+01 m
 * + 1.236E+01 m

23) Two large parallel conducting plates are separated by 7.57 mm. Equal and opposite surface charges of 7.830E-07 C/m2 exist on the surfaces between the plates. What is the distance between equipotential planes which differ by 57 V?
 * + 6.446E-01 mm
 * - 7.412E-01 mm
 * - 8.524E-01 mm
 * - 9.803E-01 mm
 * - 1.127E+00 mm

24) An empty parallel-plate capacitor with metal plates has an area of 1.89 m2, separated by 1.36 mm. How much charge does it store if the voltage is 4.040E+03 V?
 * - 3.395E+01 &mu;C
 * - 3.735E+01 &mu;C
 * - 4.108E+01 &mu;C
 * - 4.519E+01 &mu;C
 * + 4.971E+01 &mu;C

25) What is the net capacitance if C1=4.41 &mu;F, C2=4.54 &mu;F, and C3=2.91 &mu;F in the configuration shown?
 * - 3.515E+00 &mu;F
 * - 3.867E+00 &mu;F
 * - 4.254E+00 &mu;F
 * - 4.679E+00 &mu;F
 * + 5.147E+00 &mu;F

26) In the figure shown C1=17.6 &mu;F, C2=2.19 &mu;F, and C3=5.84 &mu;F. The voltage source provides &epsilon;=5.4 V. What is the charge on C1?
 * - 2.707E+01 &mu;C
 * + 2.978E+01 &mu;C
 * - 3.275E+01 &mu;C
 * - 3.603E+01 &mu;C
 * - 3.963E+01 &mu;C

27) In the figure shown C1=15.5 &mu;F, C2=2.72 &mu;F, and C3=5.1 &mu;F. The voltage source provides &epsilon;=5.89 V. What is the energy stored in C2?
 * - 8.800E+00 &mu;J
 * - 9.680E+00 &mu;J
 * + 1.065E+01 &mu;J
 * - 1.171E+01 &mu;J
 * - 1.288E+01 &mu;J

28) What is the average current involved when a truck battery sets in motion 702 C of charge in 2.92 s while starting an engine?
 * + 2.404E+02 A
 * - 2.645E+02 A
 * - 2.909E+02 A
 * - 3.200E+02 A
 * - 3.520E+02 A

29) The charge passing a plane intersecting a wire is $$Q_M=\left(1-e^{t/\tau}\right)$$, where $$Q_M$$=38 C  and $$\tau=$$0.0106 s. What is the current at $$t=$$0.0123 s?
 * - 1.021E+03 A
 * + 1.123E+03 A
 * - 1.236E+03 A
 * - 1.359E+03 A
 * - 1.495E+03 A

30) Calculate the drift speed of electrons in a copper wire with a diameter of 3.32 mm carrying a 18.4 A current, given that there is one free electron per copper atom. The density of copper is 8.80 x 103kg/m3 and the atomic mass of copper is 63.54 g/mol. Avagadro's number is 6.02 x 1023atoms/mol.
 * - 1.195E-04 m/s
 * - 1.315E-04 m/s
 * - 1.446E-04 m/s
 * + 1.591E-04 m/s
 * - 1.750E-04 m/s

31) A make-believe metal has a density of 5.880E+03 kg/m3 and an atomic mass of 73.2 g/mol. Taking Avogadro's number to be 6.020E+23 atoms/mol and assuming one free electron per atom, calculate the number of free electrons per cubic meter.
 * - 4.396E+28 e&minus;/m3
 * + 4.836E+28 e&minus;/m3
 * - 5.319E+28 e&minus;/m3
 * - 5.851E+28 e&minus;/m3
 * - 6.436E+28 e&minus;/m3

32) A device requires consumes 121 W of power and requires 5.12 A of current which is supplied by a single core 10-guage (2.588 mm diameter) wire. Find the magnitude of the average current density.
 * - 8.849E+05 A/m2
 * + 9.734E+05 A/m2
 * - 1.071E+06 A/m2
 * - 1.178E+06 A/m2
 * - 1.296E+06 A/m2

33) Calculate the resistance of a 12-gauge copper wire that is 97 m long and carries a current of 29 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.
 * + 4.923E-01 &Omega;
 * - 5.416E-01 &Omega;
 * - 5.957E-01 &Omega;
 * - 6.553E-01 &Omega;
 * - 7.208E-01 &Omega;

34) Calculate the electric field in a 12-gauge copper wire that is 75 m long and carries a current of 21 mA. The resistivity of copper is 1.680E-08 &Omega;&middot;m and 12-gauge wire as a cross-sectional area of 3.31 mm2.
 * - 7.280E-05 V/m
 * - 8.008E-05 V/m
 * - 8.809E-05 V/m
 * - 9.690E-05 V/m
 * + 1.066E-04 V/m

35) Imagine a substance could be made into a very hot filament. Suppose the resitance is 2.14 &Omega; at a temperature of 77&deg;C and that the temperature coefficient of expansion is 4.750E-03 (&deg;C)&minus;1). What is the resistance at a temperature of 542 &deg;C?
 * - 6.540E+00 &Omega;
 * + 6.867E+00 &Omega;
 * - 7.210E+00 &Omega;
 * - 7.571E+00 &Omega;
 * - 7.949E+00 &Omega;

36) A DC winch moter draws 31 amps at 191 volts as it lifts a 5.080E+03 N weight at a constant speed of 0.99 m/s. Assuming that all the electrical power is either converted into gravitational potential energy or ohmically heats the motor's coils, calculate the coil's resistance.
 * - 6.972E-01 &Omega;
 * - 7.669E-01 &Omega;
 * - 8.436E-01 &Omega;
 * + 9.280E-01 &Omega;
 * - 1.021E+00 &Omega;

37) What is consumer cost to operate one 77&minus;W incandescent bulb for 12 hours per day for 1 year (365 days) if the cost of electricity is $0.134 per kilowatt-hour?
 * - $3.087E+01
 * - $3.395E+01
 * - $3.735E+01
 * - $4.108E+01
 * + $4.519E+01

38) A given battery has a 12 V emf and an internal resistance of 0.193 &Omega;. If it is connected to a 0.89 &Omega; resistor what is the power dissipated by that load?
 * - 8.210E+01 W
 * - 9.030E+01 W
 * - 9.934E+01 W
 * + 1.093E+02 W
 * - 1.202E+02 W

39) A battery with a terminal voltage of 14.9 V is connected to a circuit consisting of 2 23.3 &Omega; resistors and one 13.6 &Omega; resistor. What is the voltage drop across the 13.6 &Omega; resistor?
 * + 3.366E+00 V
 * - 3.703E+00 V
 * - 4.073E+00 V
 * - 4.480E+00 V
 * - 4.928E+00 V

40) Three resistors, R1 = 1.7 &Omega;, and R2 = R2 = 3.75 &Omega;, are connected in parallel to a 9.74 V voltage source. Calculate the power dissipated by the smaller resistor (R1.)
 * - 4.193E+01 W
 * - 4.612E+01 W
 * - 5.073E+01 W
 * + 5.580E+01 W
 * - 6.138E+01 W

41) In the circuit shown V=19.9 V, R1=1.69 &Omega;, R2=7.02 &Omega;, and R3=12.8 &Omega;. What is the power dissipated by R2?
 * + 2.993E+01 W
 * - 3.293E+01 W
 * - 3.622E+01 W
 * - 3.984E+01 W
 * - 4.383E+01 W

42) The resistances in the figure shown are R1= 1.35 &Omega;, R2= 1.52 &Omega;, and R2= 2.45 &Omega;. V1 and V3 are text 0.419 V and 2.37 V, respectively. But V2 is opposite to that shown in the figure, or, equivalently, V2=&minus;0.511 V. What is the absolute value of the current through R1?
 * - 8.841E-02 A
 * + 9.725E-02 A
 * - 1.070E-01 A
 * - 1.177E-01 A
 * - 1.294E-01 A

43) Two sources of emf &epsilon;1=52.2 V, and  &epsilon;2=15.4 V are oriented as shownin the circuit. The resistances are R1=4.89 k&Omega; and  R2=2.76 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=2.99 mA and I4=0.693 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of I5?
 * - 1.726E+00 mA
 * - 1.898E+00 mA
 * - 2.088E+00 mA
 * + 2.297E+00 mA
 * - 2.527E+00 mA

44) Two sources of emf &epsilon;1=57.8 V, and  &epsilon;2=18.5 V are oriented as shownin the circuit. The resistances are R1=2.53 k&Omega; and  R2=1.8 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=7.15 mA and I4=1.27 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R1?
 * - 1.276E+01 V
 * - 1.404E+01 V
 * + 1.544E+01 V
 * - 1.699E+01 V
 * - 1.869E+01 V

45) Two sources of emf &epsilon;1=60.7 V, and  &epsilon;2=16.7 V are oriented as shownin the circuit. The resistances are R1=4.72 k&Omega; and  R2=2.33 k&Omega;.  Three other currents enter and exit or exit from portions of the circuit that lie outside the dotted rectangle and are not shown.  I3=4.65 mA and I4=0.946 mA enter and leave near R2, while the current I5 exits near R1.What is the magnitude (absolute value) of voltage drop across R2?
 * - 1.981E+01 V
 * + 2.180E+01 V
 * - 2.398E+01 V
 * - 2.637E+01 V
 * - 2.901E+01 V

46) In the circuit shown the voltage across the capaciator is zero at time t=0 when a switch is closed putting the capacitor into contact with a power supply of 379 V.  If the combined external and internal resistance is 158 &Omega and the capacitance is  95 mF, how long will it take for the capacitor's voltage to reach 234.0 V?
 * - 1.084E+01 s
 * - 1.192E+01 s
 * - 1.311E+01 s
 * + 1.442E+01 s
 * - 1.586E+01 s

47) An alpha-particle (q=3.2x10&minus;19C) moves through a uniform magnetic field that is parallel to the positive z-axis with magnitude 5.11 T. What is the  x-component of the force on the alpha-particle if it is moving with a velocity (8.99 i + 7.56 j  + 8.49 k) x 104 m/s?
 * - 1.124E-13 N
 * + 1.236E-13 N
 * - 1.360E-13 N
 * - 1.496E-13 N
 * - 1.645E-13 N

48) A charged particle in a magnetic field of 2.780E-04 T is moving perpendicular to the magnetic field with a speed of 6.370E+05 m/s. What is the period of orbit if orbital radius is 0.671 m?
 * - 6.017E-06 s
 * + 6.619E-06 s
 * - 7.280E-06 s
 * - 8.008E-06 s
 * - 8.809E-06 s

49) An alpha-particle (m=6.64x10&minus;27kg, q=3.2x10&minus;19C) briefly enters a uniform magnetic field of magnitude 0.0783 T . It emerges after being deflected by 64&deg; from its original direction. How much time did it spend in that magnetic field?
 * - 2.224E-07 s
 * - 2.446E-07 s
 * - 2.691E-07 s
 * + 2.960E-07 s
 * - 3.256E-07 s

50) A 18 cm-long horizontal wire is maintained in static equilibrium by a horizontally directed magnetic field that is perpendicular to the wire (and to Earth's gravity). The mass of the wire is 8 g, and the magnitude of the magnetic field is 0.351 T. What current is required to maintain this balance?
 * + 1.241E+00 A
 * - 1.365E+00 A
 * - 1.501E+00 A
 * - 1.652E+00 A
 * - 1.817E+00 A

51) A long rigind wire carries a 8 A current. What is the magnetic force per unit length on the wire if a 0.899 T magnetic field is directed 43&deg; away from the wire?
 * - 3.685E+00 N/m
 * - 4.054E+00 N/m
 * - 4.459E+00 N/m
 * + 4.905E+00 N/m
 * - 5.395E+00 N/m

52) A circular current loop of radius 2.86 cm carries a current of 1.7 mA. What is the magnitude of the torque if the dipole is oriented at 43 &deg; to a uniform magnetic fied of 0.729 T?
 * - 1.483E-06 N m
 * - 1.632E-06 N m
 * - 1.795E-06 N m
 * - 1.974E-06 N m
 * + 2.172E-06 N m

53) An electron beam (m=9.1 x 10&minus;31kg, q=1.6 x 10&minus;19C) enters a crossed-field velocity selector with magnetic and electric fields of 5.53 mT and 7.210E+03 N/C, respectively. What must the velocity of the electron beam be to transverse the crossed fields undeflected ?
 * - 8.905E+05 m/s
 * - 9.796E+05 m/s
 * - 1.078E+06 m/s
 * - 1.185E+06 m/s
 * + 1.304E+06 m/s

54) The silver ribbon shown are a=4.65 cm, b=3.92 cm, and c= 1.23 cm. The current carries a current of 89 A and it lies in a uniform magnetic field of 2.4 T.  Using the density of 5.900E+28 electrons per cubic meter for silver, find the Hallpotential between the edges of the ribbon.
 * - 1.255E-06 V
 * - 1.380E-06 V
 * - 1.518E-06 V
 * - 1.670E-06 V
 * + 1.837E-06 V

55) A cyclotron used to accelerate alpha particlesm=6.64 x 10&minus;27kg, q=3.2 x 10&minus;19C) has a radius of 0.398 m and a magneticfield of 0.855 T. What is their maximum kinetic energy?
 * + 5.581E+00 MeV
 * - 6.139E+00 MeV
 * - 6.753E+00 MeV
 * - 7.428E+00 MeV
 * - 8.171E+00 MeV

56) A wire carries a current of 316 A in a circular arc with radius 1.55 cm swept through 76 degrees. Assuming that the rest of the current is 100% shielded by  mu-metal, what is the magnetic field at the center of the arc?
 * - 8.070E+00 Tesla
 * + 8.878E+00 Tesla
 * - 9.765E+00 Tesla
 * - 1.074E+01 Tesla
 * - 1.182E+01 Tesla

57) Three wires sit at the corners of a square of length 0.811 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (2.18 A, 1.44 A, 1.46 A), respectively. What is the x-component of the magnetic field at point P?
 * - Bx= 4.887E-05 T
 * + Bx= 5.376E-05 T
 * - Bx= 5.914E-05 T
 * - Bx= 6.505E-05 T
 * - Bx= 7.156E-05 T

58) Three wires sit at the corners of a square of length 0.762 cm. The currents all are in the positive-z direction (i.e. all come out of the paper in the figure shown.) The currents (I1, I2, I2) are (1.69 A, 1.7 A, 1.02 A), respectively. What is the y-component of the magnetic field at point P?
 * - By= 5.510E-05 T
 * - By= 6.061E-05 T
 * + By= 6.667E-05 T
 * - By= 7.333E-05 T
 * - By= 8.067E-05 T

59) Two parallel wires each carry a 5.0 mA current and are oriented in the z direction. The first wire is located in the x-y   plane at (4.48 cm, 0.973 cm), while the other is located at (3.32 cm, 4.79 cm). What is the force per unit length between the wires?
 * - 1.139E-10 N/m
 * + 1.253E-10 N/m
 * - 1.379E-10 N/m
 * - 1.517E-10 N/m
 * - 1.668E-10 N/m

60) Two loops of wire carry the same current of 62 kA, and flow in the same direction. They share a common axis and orientation.  One loop has a radius of 0.584 m while the other has a radius of 1.38 m.  What is the magnitude of the magnetic field at a point on the axis of both loops, situated between the loops at a distance 0.341 m from the first (smaller) loopif the disance between the loops is 1.21 m?
 * - 4.102E-02 T
 * - 4.513E-02 T
 * - 4.964E-02 T
 * - 5.460E-02 T
 * + 6.006E-02 T

61) Under most conditions the current is distributed uniformly over the cross section of the wire.  What is the magnetic field 1.34 mm from the center of a wire of radius 3 mm if the current is 1A?
 * - 2.237E-05 T
 * - 2.461E-05 T
 * - 2.707E-05 T
 * + 2.978E-05 T
 * - 3.276E-05 T

62) The Z-pinch is an (often unstable) cylindrical plasma in which a aximuthal magnetic field is produced by a current in the z direction. A simple model for the magnetic field, valid for $$r<a$$ is, $$B_\theta (r)=\left( \frac{2r}{a} - \frac{r^2}{a^2}\right)B_{max}$$, where $$B_{max}$$ is the maximum magnetic field (at $$r=a$$).  If $$a=$$ 0.703 m and $$B_{max}=\,$$ 0.521 T, then how much current (in the z-direction) flows through a circle of radius $$r=$$ 0.165 m that is centered on the axis with its plane perpendicular to the axis?
 * - 1.338E+05 A
 * - 1.472E+05 A
 * - 1.619E+05 A
 * + 1.781E+05 A
 * - 1.959E+05 A

63) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.39 kA, I2=2.19 kA, and I3=3.68 kA, take the $$\beta$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:
 * - 1.547E-03 T-m
 * - 1.702E-03 T-m
 * + 1.872E-03 T-m
 * - 2.060E-03 T-m
 * - 2.266E-03 T-m

64) The numbers (1,2,3) in the figure shown represent three currents flowing in or out of the page: I1 and I3 flow out of the page, and I2 flows into the page, as shown. Two closed paths are shown, labeled $$\beta$$ and $$\omega$$. If  I1=2.37 kA, I2=1.05 kA, and I3=2.99 kA, take the $$\omega$$ path and evalulate the line integral,    $$\oint\vec B\cdot d\vec\ell$$:
 * - 4.069E-03 T-m
 * - 4.476E-03 T-m
 * - 4.924E-03 T-m
 * + 5.416E-03 T-m
 * - 5.958E-03 T-m

65) A solenoid has 8.230E+04 turns wound around a cylinder of diameter 1.5 cm and length 18 m. The current through the coils is 0.633 A.  Define the origin to be the center of the solenoid and neglect end effects as you calculate the line integral $$\int\vec B\cdot\vec\ell$$ alongthe axis from z=&minus;3.74 cm to z=+3.23 cm
 * - 1.731E-04 T-m
 * - 1.905E-04 T-m
 * - 2.095E-04 T-m
 * - 2.305E-04 T-m
 * + 2.535E-04 T-m

66) A long coil is tightly wound around a (hypothetical) ferromagnetic cylinder. If n= 20 turns per centimeter and the current applied to the solenoid is 598 mA, the net magnetic field is measured to be 1.38 T. What is the magnetic susceptibility for this case?
 * - $$\chi \text{ (chi) }=$$ 8.338E+02
 * + $$\chi \text{ (chi) }=$$ 9.172E+02
 * - $$\chi \text{ (chi) }=$$ 1.009E+03
 * - $$\chi \text{ (chi) }=$$ 1.110E+03
 * - $$\chi \text{ (chi) }=$$ 1.221E+03

67) A square coil has sides that are L= 0.673 m long and is tightly wound with N=211 turns of wire. The resistance of the coil is R=5.31 &Omega;. The coil is placed in a spacially uniform magnetic field that is directed perpendicular to the face of the coil and whose magnitude is increasing at a rate dB/dt=0.0454 T/s. If R represents the only impedance of the coil, what is the magnitude of the current circulting through it?
 * - 6.753E-01 A
 * - 7.428E-01 A
 * + 8.171E-01 A
 * - 8.988E-01 A
 * - 9.887E-01 A

68) A time dependent magnetic field is directed perpendicular to the plane of a circular coil with a radius of 0.317 m. The magnetic field is spatially uniform but decays in time according to $$(3.5)e^{-\alpha t}$$, where $$\alpha=$$6.25 s. What is the current in the coil if the impedance of the coil is 52.3 &Omega;?
 * - 6.717E-02 A
 * - 7.388E-02 A
 * - 8.127E-02 A
 * + 8.940E-02 A
 * - 9.834E-02 A

69) The current through the windings of a solenoid with n= 2.120E+03 turns per meter is changing at a rate dI/dt=4 A/s. The solenoid is 94 cm long and has a cross-sectional diameter of 2.56 cm.  A small coil consisting of N=30turns wraped in a circle of diameter 1.15 cm is placed in the middle of the solenoid such that the plane of the coil is perpendicular to the central axis of the solenoid. Assume that the infinite-solenoid approximation is valid inside the small coil.  What is the emf induced in the coil?
 * - 3.019E-05 V
 * + 3.321E-05 V
 * - 3.653E-05 V
 * - 4.018E-05 V
 * - 4.420E-05 V

70) Calculate the motional emf induced along a 40.1 km conductor moving at an orbital speed of 7.85 km/s perpendicular to Earth's 5.160E-05 Tesla magnetic field.
 * - 1.477E+04 V
 * + 1.624E+04 V
 * - 1.787E+04 V
 * - 1.965E+04 V
 * - 2.162E+04 V

71) A cylinder of height 1.98 cm and radius 2.62 cm is cut into a wedge as shown. Now imagine that the volume grows as &theta; increases while the radius R and height h remains constant. What is the volume's rate of change if point P is 1.33 cm from point O and moves at a speed of 2.0 cm/s? Assume that the wedge grows in such a way as the front face moves by rotating around the axis (that contains point O.) --(Answer & Why this question is different.)
 * - 6.980E+00 cm3/s
 * - 7.678E+00 cm3/s
 * - 8.446E+00 cm3/s
 * - 9.290E+00 cm3/s
 * + 1.022E+01 cm3/s

72) A recangular coil with an area of 0.371 m2 and 20 turns is placed in a uniform magnetic field of 2.51 T. The coil is rotated about an axis that is perpendicular to this field. At time t=0 the normal to the coil is oriented parallel to the magnetic field and the coil is rotating with a constant angular frequency of 3.060E+03 s&minus;1.  What is the magnitude (absolute value) of the induced emf at t = 88 s?
 * + 5.694E+04 V
 * - 6.263E+04 V
 * - 6.889E+04 V
 * - 7.578E+04 V
 * - 8.336E+04 V

73) A spatially uniform magnetic points in the z-direction and oscilates with time as $$\vec B(t) = B_0\sin\omega t $$ where $$B_0=$$3.26 T and $$\omega=$$9.250E+03 s&minus;1. Suppose the electric field is always zero at point $$\mathcal O$$, and consider a circle of radius 0.385 m that is centered at that point and oriented in a plane perpendicular to the magnetic field. Evaluate the maximum value of the line integral $$\oint \vec B\cdot d\vec s$$ around the circle.
 * - 6.029E+04 V
 * - 6.631E+04 V
 * + 7.295E+04 V
 * - 8.024E+04 V
 * - 8.826E+04 V

74) A long solenoid has a radius of 0.442 m and 63 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$22 s&minus;1.What is the induced electric fied at a distance 1.94 m from the axis at time t=0.0331 s ?
 * + 2.964E-04 V/m
 * - 3.260E-04 V/m
 * - 3.586E-04 V/m
 * - 3.945E-04 V/m
 * - 4.339E-04 V/m

75) A long solenoid has a radius of 0.508 m and 90 turns per meter; its current decreases with time according to $$I_0e^{-\alpha t}$$, where $$I_0=$$7 A and $$\alpha=$$25 s&minus;1.What is the induced electric fied at a distance 0.145 m from the axis at time t=0.0643 s ?
 * - 2.614E-04 V/m
 * + 2.875E-04 V/m
 * - 3.163E-04 V/m
 * - 3.479E-04 V/m
 * - 3.827E-04 V/m

76) A long solenoid has a length 0.714 meters, radius 4.95 cm, and 578 turns. It surrounds  coil of radius 8.72 meters and 16turns.  If the current in the solenoid is changing at a rate of 248 A/s, what is the emf induced in the surounding coil?
 * - 6.667E-02 V
 * - 7.334E-02 V
 * - 8.067E-02 V
 * - 8.874E-02 V
 * + 9.762E-02 V

77) An induced emf of 4.82V is measured across a coil of 73 closely wound turns while the current throuth it increases uniformly from 0.0 to 4.61A in 0.934s. What is the self-inductance of the coil?
 * - 7.337E-01 H
 * - 8.071E-01 H
 * - 8.878E-01 H
 * + 9.765E-01 H
 * - 1.074E+00 H

78) A washer has an inner diameter of 2.57 cm and an outer diamter of 4.14 cm. The thickness is $$h=Cr^{-n}$$ where $$r$$ is measured in cm, $$C=4.33mm$$, and $$n=2.42$$. What is the volume of the washer?
 * - 7.226E-01 cm3
 * - 7.949E-01 cm3
 * - 8.744E-01 cm3
 * - 9.618E-01 cm3
 * + 1.058E+00 cm3

79) Suppose switch S1 is suddenly closed at time t=0 in the figure shown. What is the current at t =1.98 s if &epsilon; = 5.75 V, R = 8.07 &Omega;, and L = 2.84 H?
 * - 4.109E-01 V
 * - 4.930E-01 V
 * - 5.917E-01 V
 * + 7.100E-01 V
 * - 8.520E-01 V

80) Suppose switch S1 in the figure shown was closed and remained closed long enough to acheive steady state. At t=0 S1 is  opened as as S2 is closed.  How long will it take for the energy stored in the inductor to be reduced to 1.79% of its maximum value if &epsilon; = 8.03 V, R = 2.4 &Omega;, and L = 1.72 H?
 * + -1.442E+00 s
 * - -1.586E+00 s
 * - -1.744E+00 s
 * - -1.919E+00 s
 * - -2.111E+00 s

81) In an LC circuit, the self-inductance is 0.0134 H and the capacitance is 3.280E-06 F. At t=0 all the energy is stored in the capacitor, which has a charge of 5.930E-05 C. How long does it take for the capacitor to become completely discharged?
 * - 2.722E-04 s
 * - 2.994E-04 s
 * + 3.293E-04 s
 * - 3.622E-04 s
 * - 3.985E-04 s

82) An ac generator produces an emf of amplitude 78 V at a frequency of 45 Hz. What is the maximum amplitude of the current if the generator is connected to a  60 mF inductor?
 * - 3.140E+00 A
 * - 3.454E+00 A
 * - 3.800E+00 A
 * - 4.180E+00 A
 * + 4.598E+00 A

83) An ac generator produces an emf of amplitude 64 V at a frequency of 95 Hz. What is the maximum amplitude of the current if the generator is connected to a  99 mF capacitor?
 * - 3.126E+00 A
 * - 3.438E+00 A
 * + 3.782E+00 A
 * - 4.160E+00 A
 * - 4.576E+00 A

84) The output of an ac generator connected to an RLC series combination has a frequency of 510 Hz and an amplitude of 0.69 V;. If R =4 &Omega;, L= 4.30E-03H, and C=9.20E-04 F, what is the impedance?
 * - 1.054E+01 &Omega;
 * - 1.159E+01 &Omega;
 * - 1.275E+01 &Omega;
 * + 1.402E+01 &Omega;
 * - 1.542E+01 &Omega;

85) The output of an ac generator connected to an RLC series combination has a frequency of 480 Hz and an amplitude of 0.17 V;. If R =5 &Omega;, L= 6.70E-03H, and C=6.30E-04 F, what is the magnitude (absolute value) of the phase difference between current and emf?
 * + 1.322E+00 &rad;
 * - 1.454E+00 &rad;
 * - 1.600E+00 &rad;
 * - 1.760E+00 &rad;
 * - 1.936E+00 &rad;

86) The output of an ac generator connected to an RLC series combination has a frequency of 8.20E+04 Hz and an amplitude of 4 V. If R =5 &Omega;, L= 5.40E-03H, and C=9.80E-06 F, what is the rms power transferred to the resistor?
 * - 1.865E-04 Watts
 * + 2.051E-04 Watts
 * - 2.256E-04 Watts
 * - 2.482E-04 Watts
 * - 2.730E-04 Watts

87) An RLC series combination is driven with an applied voltage of of V=V0sin(&omega;t), where V0=0.38 V. The resistance, inductance, and capacitance are R =7 &Omega;, L= 4.10E-03H, and C=7.40E-04 F, respectively. What is the amplitude of the current?
 * - 4.486E-02 A
 * - 4.935E-02 A
 * + 5.429E-02 A
 * - 5.971E-02 A
 * - 6.569E-02 A

88) The quality factor Q is a dimensionless paramater involving the relative values of the magnitudes of the at three impedances (R, XL, XC). Since Q is calculatedat resonance, XL,  XC and only twoimpedances are involved,  Q=&equiv;&omega;0L/R is definedso that Q is large if the resistance is low.  Calculate the Q of an LRC series driven at resonance by an applied voltage of of V=V0sin(&omega;t), where V0=1 V. The resistance, inductance, and capacitance are R =0.21 &Omega;, L= 4.80E-03H, and C=3.60E-06 F, respectively.
 * + Q = 1.739E+02
 * - Q = 2.000E+02
 * - Q = 2.300E+02
 * - Q = 2.645E+02
 * - Q = 3.041E+02

89) A step-down transformer steps 19 kV down to 220 V. The high-voltage input is provided by a 250 &Omega; power line that carries 4 A of currentWhat is the output current (at the 220 V side ?)
 * - 2.595E+02 A
 * - 2.855E+02 A
 * - 3.140E+02 A
 * + 3.455E+02 A
 * - 3.800E+02 A

90) A parallel plate capacitor with a capicatnce C=5.40E-06 F whose plates have an area A=3.50E+03 m2 and separation d=5.70E-03 m is connected via a swith to a 92 &Omega; resistor and a battery of voltage V0=52 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the voltage at time t=2.40E-03?
 * - 3.876E+01 V
 * - 4.263E+01 V
 * - 4.690E+01 V
 * + 5.159E+01 V
 * - 5.674E+01 V

91) A parallel plate capacitor with a capicatnce C=1.10E-06 F whose plates have an area A=930.0 m2 and separation d=7.50E-03 m is connected via a swith to a 83 &Omega; resistor and a battery of voltage V0=42 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the electric field at time t=3.80E-04?
 * - 3.765E+03 V/m
 * - 4.142E+03 V/m
 * - 4.556E+03 V/m
 * - 5.012E+03 V/m
 * + 5.513E+03 V/m

92) A parallel plate capacitor with a capicatnce C=3.80E-06 F whose plates have an area A=1.80E+03 m2 and separation d=4.30E-03 m is connected via a swith to a 41 &Omega; resistor and a battery of voltage V0=39 V as shown in the figure. The current starts to flow at time t=0 when the switch is closed. What is the magnitude of the displacement current at time t=3.60E-04?
 * - 7.089E-02 A
 * - 7.798E-02 A
 * - 8.578E-02 A
 * + 9.436E-02 A
 * - 1.038E-01 A

93) A 46 kW radio transmitter on Earth sends it signal to a satellite 140 km away. At what distance in the same direction would the signal have the same maximum field strength if the transmitter's output power were increased to 73 kW?
 * + 1.764E+02 km
 * - 1.940E+02 km
 * - 2.134E+02 km
 * - 2.347E+02 km
 * - 2.582E+02 km

94) What is the radiation pressure on an object that is 5.90E+11 m away from the sun and has cross-sectional area of 0.014 m2? The average power output of the Sun is 3.80E+26 W.
 * - 5.268E-07 N/m2
 * + 5.795E-07 N/m2
 * - 6.375E-07 N/m2
 * - 7.012E-07 N/m2
 * - 7.713E-07 N/m2

95) What is the radiation force on an object that is 5.20E+11 m away from the sun and has cross-sectional area of 0.04 m2? The average power output of the Sun is 3.80E+26 W.
 * - 2.242E-08 N
 * - 2.466E-08 N
 * - 2.713E-08 N
 * + 2.984E-08 N
 * - 3.283E-08 N