Wright State University Lake Campus/2016-9/Phy2410/Study guide/Pdf

S_G: Studyguide
phc20160712T125120 1) The temperature is -3 degrees Celsius, and you are standing 0.66 km from a cliff. What is the echo time?
 * a) 2.949 x 100 seconds
 * b) 3.184 x 100 seconds
 * c) 3.438 x 100 seconds
 * d) 3.713 x 100 seconds
 * e) 4.009 x 100 seconds

2) While standing 0.76 km from a cliff, you measure the echo time to be 4.339 seconds. What is the temperature?
 * a) 2.83 x 101Celsius
 * b) 3.26 x 101Celsius
 * c) 3.77 x 101Celsius
 * d) 4.35 x 101Celsius
 * e) 5.03 x 101Celsius

3) What is the speed of a transverse wave on a string if the string is 1.19 m long, clamped at both ends, and harmonic number 6 has a frequency of 834 Hz?
 * a) 2.25 x 102 unit
 * b) 2.73 x 102 unit
 * c) 3.31 x 102 unit
 * d) 4.01 x 102 unit
 * e) 4.86 x 102 unit

4) Integrate the line integral of, $$\vec F = 6.1xy\hat x + 5.9y^3\hat y $$, along the y axis from  y = 6 to y = 12
 * a) 2.87E+04
 * b) 3.07E+04
 * c) 3.28E+04
 * d) 3.51E+04
 * e) 3.76E+04

5) Integrate the function, $$\vec F = r^9\theta^3\hat r + r^8\theta^ 7\hat \theta$$, along the first quadrant of a circle of radius 4
 * a) 1.14E+06
 * b) 1.21E+06
 * c) 1.30E+06
 * d) 1.39E+06
 * e) 1.49E+06

6) Integrate the line integral of $$\vec F = 3.8xy\hat x + 5.1x\hat y $$  from the origin to the point at x = 2.5 and y = 3.2
 * a) 4.27E+01
 * b) 4.57E+01
 * c) 4.89E+01
 * d) 5.24E+01
 * e) 5.60E+01

7) Integrate the function, $$\vec F = -x^3y^5\hat x + x^2y^3\hat y$$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule
 * a) 3.81E-01
 * b) 4.08E-01
 * c) 4.37E-01
 * d) 4.67E-01
 * e) 5.00E-01

8) What is the magnitude of the electric field at the origin if a 1.7 nC charge is placed at x = 6.4 m, and a 3 nC charge is placed at y = 8 m?
 * a) 4.22 x 10-1N/C
 * b) 4.87 x 10-1N/C
 * c) 5.63 x 10-1N/C
 * d) 6.5 x 10-1N/C
 * e) 7.51 x 10-1N/C

9) What angle does the electric field at the origin make with the x-axis if a 1.8 nC charge is placed at x = -6.9 m, and a 2.5  nC charge is placed at y = -7.5 m?
 * a) 2.79 x 101degrees
 * b) 3.22 x 101degrees
 * c) 3.72 x 101degrees
 * d) 4.3 x 101degrees
 * e) 4.96 x 101degrees

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at  (x,y) =( 4a, 6a) is &beta;kQ/a2, where &beta; equals
 * a) 1.52 x 10-4 unit
 * b) 1.85 x 10-4 unit
 * c) 2.24 x 10-4 unit
 * d) 2.71 x 10-4 unit
 * e) 3.28 x 10-4 unit

11) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at  (x,y) =( 1.1a, 1.2a) is &beta;kQ/a2, where &beta; equals
 * a) 1.61 x 10-1 unit
 * b) 1.95 x 10-1 unit
 * c) 2.36 x 10-1 unit
 * d) 2.86 x 10-1 unit
 * e) 3.47 x 10-1 unit

12) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal B=$$
 * a) 3
 * b) &minus;3
 * c) &minus;7
 * d) &minus;3
 * e) 2

13) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) s&minus;1
 * b) 5
 * c) s&minus;4
 * d) 1&minus;s
 * e) 5&minus;s

14) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal F=$$:
 * a) 3
 * b) 2/3
 * c) 3/2
 * d) 1/2
 * e) 2

15) A line of charge density &lambda; situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) s&minus;3
 * b) s&minus;7
 * c) 7&minus;s
 * d) 3&minus;s
 * e) 8

16) A line of charge density &lambda; situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:
 * a) 72 + (3&minus;s)2
 * b) 72 + 82
 * c) (7-s)2 + 82
 * d) 32 + 82
 * e) 72 + (8&minus;s)2

17) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$
 * a) 3&minus;s
 * b) 7&minus;s
 * c) s&minus;3
 * d) s&minus;7
 * e) 3

18) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where$$\mathcal F=$$
 * a) 3
 * b) 2
 * c) 3/2
 * d) 1/2

19) A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) 2 &minus; s
 * b) 9 &minus; s
 * c) s &minus; 9
 * d) s &minus; 2
 * e) 2

20) A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:
 * a) 72 + (2-s)2
 * b) 22 + (7-s)2
 * c) 92 + (2-s)2
 * d) 22 + (9-s)2
 * e) 92 + (7-s)2

21) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal A=$$:
 * a) 8
 * b) 2
 * c) 1/2
 * d) 4

22) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) s&minus;8
 * b) s&minus;4
 * c) 4&minus;s
 * d) 4
 * e) 8&minus;s

23) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) 4&minus;s
 * b) s&minus;4
 * c) s&minus;8
 * d) 8&minus;s
 * e) 4

24) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * a) 5
 * b) 1&minus;s
 * c) 5&minus;s
 * d) s&minus;4
 * e) s&minus;1

25) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. The height is much less than the radius: H << R. The electric field at the center vanishes.  What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
 * a)b) $$\varepsilon_0 E=  H\rho $$
 * b)c) $$\varepsilon_0 E=  H\rho z$$
 * c)d) none of these are correct
 * d)e) $$\varepsilon_0 E = H\rho /2$$
 * e) $$\varepsilon_0 E=   \rho z $$

26) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. The height is much less than the radius: H << R. The electric field at the center vanishes.  What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
 * a)b) none of these are correct
 * b)c) $$\varepsilon_0 E=   \rho z $$
 * c)e) $$\varepsilon_0 E=  H\rho z$$
 * d)d) $$\varepsilon_0 E=  H\rho $$
 * e) $$\varepsilon_0 E = H\rho /2$$

27) A sphere has a uniform charge density of $$\rho$$, and a radius or R. What formula describes the electric field at a distance r > R?
 * a)d) $$ r^2\varepsilon_0 E=r^3\rho /2$$
 * b)e) $$ r^2\varepsilon_0 E=R^3\rho /3$$
 * c)b) $$ r^2\varepsilon_0 E=R^3\rho /2$$
 * d) none of these are correct
 * e)c) $$ r^2\varepsilon_0 E= r^3\rho/3$$

28) A sphere has a uniform charge density of $$\rho$$, and a radius equal to R. What formula describes the electric field at a distance r < R?
 * a)b) $$ r^2\varepsilon_0 E=R^3\rho /3$$
 * b)c) none of these are correct
 * c) $$ r^2\varepsilon_0 E=r^3\rho /2$$
 * d)e) $$ r^2\varepsilon_0 E=R^3\rho /2$$
 * e)d) $$ r^2\varepsilon_0 E=r^3\rho /3$$

29) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. The height is much greater than the radius: H >> R. The electric field at the center vanishes.  What formula describes the electric field at a distance, r, radially from the center if r < R?
 * a)e) $$2r^2\varepsilon_0 E= R^3  \rho $$
 * b)d) none of these are correct
 * c)c) $$2\varepsilon_0 E = r\rho $$
 * d) $$2R\varepsilon_0 E=  r^2\rho $$
 * e)b) $$2r\varepsilon_0 E = R^2\rho $$

30) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. The height is much greater than the radius: H >> R. The electric field at the center vanishes.  What formula describes the electric field at a distance, r, radially from the center if r > R?
 * a)e) $$2r^2\varepsilon_0 E= R^3  \rho $$
 * b)b) $$2\varepsilon_0 E = r\rho $$
 * c)d) none of these are correct
 * d) $$2R\varepsilon_0 E=  r^2\rho $$
 * e)c) $$2r\varepsilon_0 E = R^2\rho $$

31) A parallel plate capacitor has both plates with an area of 1.45 m2. The separation between the plates is  1.53mm.  Applied to the plates is a potential difference of 2.55 kV.  What is the capacitance?
 * a) 8.39 nF.
 * b) 9.65 nF.
 * c) 11.1 nF.
 * d) 12.76 nF.
 * e) 14.68 nF.

32) The same parallel plate capacitor, with area 1.15 m2, plate separation  0.63mm, and an applied voltage of 2.25 kV.  How much charge is stored?
 * a) 23.91 &mu;C.
 * b) 27.5 &mu;C.
 * c) 31.62 &mu;C.
 * d) 36.37 &mu;C.
 * e) 41.82 &mu;C.

33) A 1.4 Farad capacitor is charged with 1.1 Coulombs. What is the value of the electric field if the plates are 0.6 mm apart?
 * a) 0.86 kV/m.
 * b) 0.99 kV/m.
 * c) 1.14 kV/m.
 * d) 1.31 kV/m.
 * e) 1.51 kV/m.

34) A 0.8 Farad capacitor charged with 1.7 Coulombs. What is the energy stored in the capacitor if the plates are 0.5 mm apart?
 * a) 1.81 J.
 * b) 2.08 J.
 * c) 2.39 J.
 * d) 2.75 J.
 * e) 3.16 J.

35) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the force between the plates if they are 0.3 mm apart?
 * a) 4025 N.
 * b) 4628 N.
 * c) 5322 N.
 * d) 6121 N.
 * e) 7039 N.

36) How fast is a 2493 eV electron moving?
 * a) 1.3 x 107 m/s.
 * b) 2 x 107 m/s.
 * c) 3 x 107 m/s.
 * d) 4.4 x 107 m/s.
 * e) 6.7 x 107 m/s.

37) A proton is accellerated (at rest) from a plate held at 767.8 volts to a plate at zero volts. What is the final speed?
 * a) 1.1 x 105 m/s.
 * b) 1.7 x 105 m/s.
 * c) 2.6 x 105 m/s.
 * d) 3.8 x 105 m/s.
 * e) 5.8 x 105 m/s.

38) What voltage is required accelerate an electron at rest to a speed of 5.6 x 104 m/s?
 * a) 5.9 x 10-3 volts
 * b) 8.9 x 10-3 volts
 * c) 1.3 x 10-2 volts
 * d) 2 x 10-2 volts
 * e) 3 x 10-2 volts

39) What voltage is required to stop a proton moving at a speed of 5.2 x 107 m/s?
 * a) 9.4 x 106 volts
 * b) 1.4 x 107 volts
 * c) 2.1 x 107 volts
 * d) 3.2 x 107 volts
 * e) 4.8 x 107 volts

40) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,  $$\vec\mathfrak F = (1.85+1.33z)\rho^3\hat\rho +7.52z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the top surface of the cylinder.
 * a) 1.304E+03
 * b) 1.579E+03
 * c) 1.914E+03
 * d) 2.318E+03
 * e) 2.809E+03

41) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,  $$\vec\mathfrak F = (2.14+2.8z)\rho^2\hat\rho +9.94z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{side}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the curved side surface of the cylinder.
 * a) 2.420E+02
 * b) 2.931E+02
 * c) 3.551E+02
 * d) 4.303E+02
 * e) 5.213E+02

42) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,  $$\vec\mathfrak F = (2.17+1.5z)\rho^2\hat\rho +8.75z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\oint\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the entire surface of the cylinder.
 * a) 3.60E+02
 * b) 4.36E+02
 * c) 5.29E+02
 * d) 6.40E+02
 * e) 7.76E+02

43) A 3.9 volt battery moves 90 Coulombs of charge in 2.2 hours. What is the power?
 * a) 4.43 x 10-2 W
 * b) 5.37 x 10-2 W
 * c) 6.51 x 10-2 W
 * d) 7.88 x 10-2 W
 * e) 9.55 x 10-2 W

44) The diameter of a copper wire is 7.4 mm, and it carries a current of 38 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
 * a) 3.07 x 10-5m/s
 * b) 3.72 x 10-5m/s
 * c) 4.5 x 10-5m/s
 * d) 5.46 x 10-5m/s
 * e) 6.61 x 10-5m/s

45) A 171 Watt DC motor draws 0.47 amps of current. What is effective resistance?
 * a) 7.74 x 102 &Omega;
 * b) 9.38 x 102 &Omega;
 * c) 1.14 x 103 &Omega;
 * d) 1.38 x 103 &Omega;
 * e) 1.67 x 103 &Omega;

46) A power supply delivers 169 watts of power to a 219 ohm resistor.  What was the applied voltage?
 * a) 8.93 x 101 volts
 * b) 1.08 x 102 volts
 * c) 1.31 x 102 volts
 * d) 1.59 x 102 volts
 * e) 1.92 x 102 volts

47) 3 amps flow through a 1 Ohm resistor. What is the voltage?}
 * a) $$3V$$
 * b) $$\frac{1}{3}V$$
 * c) $$1V$$
 * d) None these are correct.

48) A 1 ohm resistor has 5 volts DC across its terminals. What is the current (I) and the power consumed?}
 * a) I = 5A &  P = 25W.
 * b) I = 5A &  P = 3W.
 * c) I = 5A &  P = 5W.
 * d) I = 5A &  P = 9W

49) The voltage across two resistors in series is 10 volts. One resistor is twice as large as the other. What is the voltage across the larger resistor? What is the voltage across the smaller one? }
 * a) $$V_{Big-Resistor} = 6.67V$$ and $$V_{small-Resistor} = 3.33V$$.
 * b) $$V_{Big-Resistor} = 3.33V$$ and$$V_{small-Resistor} = 6.67V$$.
 * c) $$V_{small-Resistor} = 5V$$ and $$V_{Big-Resistor} = 5V$$.
 * d) None of these are true.

50) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in series. What is the total resistance?}
 * a) $$R_{Total} = 0.5454\Omega$$.
 * b) None of these are true.
 * c) $$R_{Total} = 3\Omega$$.
 * d) $$R_{Total} = 6\Omega$$.

51) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?}
 * a) $$R_1 = 250V$$ and $$R_2 = 0V$$.
 * b) None of these are true.
 * c) $$R_1 = 125V$$ and $$R_2 = 125V$$.
 * d) $$R_1 = 150V$$ and $$R_2 = 100V$$.

52) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in parallel. What is the total resistance?}
 * a) $$\frac{6}{3}\Omega$$.
 * b) $$\frac{3}{6}\Omega$$.
 * c) $$\frac{11}{6}\Omega$$.
 * d) $$\frac{6}{11}\Omega$$.

53) A 5 ohm and a 2 ohm resistor are connected in parallel. What is the total resistance?}
 * a) $$\frac{10}{7}\Omega$$.
 * b)  $$\frac{6}{10}\Omega$$.
 * c) $$\frac{7}{10}\Omega$$.
 * d) $$\frac{10}{6}\Omega$$.

54) A 7 ohm and a 3 ohm resistor are connected in parallel. What is the total resistance?}
 * a) $$\frac{21}{10}\Omega$$.
 * b) $$\frac{10}{21}\Omega$$.
 * c) $$\frac{11}{7}\Omega$$.
 * d) $$\frac{7}{11}\Omega$$.

55) Three 1 ohm resistors are connected in parallel. What is the total resistance?}
 * a) $$\frac{2}{3}\Omega$$.
 * b) $$\frac{3}{2}\Omega$$.
 * c) $$ 3\Omega$$.
 * d) $$\frac{1}{3}\Omega$$.

56) If you put an infinite number of resistors in parallel, what would the total resistance be?}
 * a)  $$R_{total}$$ would approach Zero as The No. of Resistors In parallel Approaches Infinity.
 * b)  None of these are true.
 * c) It is not possible to connect that Number of Resistors in parallel.
 * d) $$R_{total}$$ would approach 1 as The No. of Resistors In parallel Approaches Infinity

57) What is the current through R1 and R2 in the figure shown?
 * a) $$I_1 = 1A$$ and $$I_2 = 25A$$.
 * b)  $$I_1 = 10A$$ and $$I_2 = 16.67A$$.
 * c)  $$I_1 = 1A$$ and $$I_2 = 1.667A$$.
 * d)  $$I_1 = 0.1A$$ and $$I_2 = 0.1667A$$.

58) Why do we say the "voltage across" or "the voltage with respect to?" Why can't we just say voltage?}
 * a) None these are correct
 * b) Voltage is a measure of Electric Potential difference between two electrical points.
 * c) It's an Electrical Cliche.
 * d) The other point could be Negative or positive.

59) What is the current through R1, R2, R3, and R4 in the figure shown?
 * a)  $$I_1 = 10A$$; $$I_2 = 50A$$; $$I_3 = 33A$$; $$I_4 = 25A$$..
 * b) $$I_1 = 1A$$; $$I_2 = 5A$$; $$I_3 = 3.3A$$; $$I_4 = 2.5A$$.
 * c) $$I_1 = 1A$$; $$I_2 = 0.5A$$; $$I_3 = 0.33A$$; $$I_4 = 0.25A$$.
 * d) $$I_1 = 0.25A$$; $$I_2 = 0.33A$$; $$I_3 = 0.5A$$; $$I_4 = 0.1A$$.

60) Two resistors are in parallel with a voltage source. How do their voltages compare?}
 * a) The voltage across both resistors is half the voltage of the source.
 * b) The voltage across both resistors is the same as the source.
 * c) None of these are true.
 * d) One has full voltage, the other has none.

61) A resistor consumes 5 watts, and its current is 10 amps. What is its voltage?
 * a) 15V.
 * b) 2V.
 * c) 10V.
 * d) 0.5V.

62) A resistor has 10 volts across it and 4 amps going through it. What is its resistance?}
 * a) None of these are true.
 * b) $$3.5\Omega.$$
 * c) $$4.5\Omega.$$
 * d) $$2.5\Omega.$$

63) If you plot voltage vs. current in a circuit, and you get a linear line, what is the significance of the slope? }
 * a) Resistance.
 * b) Discriminant.
 * c) Power.
 * d) None of these are true.

64) A resistor has 3 volts across it. Its resistance is 1.5 ohms. What is the current?}
 * a) 12A
 * b) 1.5A
 * c) 3A
 * d) 2A

65) A resistor has 8 volts across it and 3 Amps going through it. What is the power consumed?}
 * a) 8W
 * b) 2.2W
 * c) 3W
 * d) 24W

66) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed? }
 * a) None of these are ture.
 * b) 11.67 Joules
 * c) 1.67 Watts
 * d) 2.5 Watts

67) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?}
 * a) 3 Joules
 * b) None of these are true
 * c) 5 Joules
 * d) 25 Joules

68) An ideal 3.1 V voltage source is connected to two resistors in parallel.  One is 1.5$$k\Omega$$, and the other is 2.2 $$k\Omega$$.  What is the current through the larger resistor?
 * a) 0.55 mA.
 * b) 0.63 mA.
 * c) 0.73 mA.
 * d) 0.84 mA.
 * e) 0.96 mA.

69) A 7 ohm resistor is connected in series to a pair of 3.4 ohm resistors that are in parallel.  What is the net resistance?
 * a) 6.6 ohms.
 * b) 7.6 ohms.
 * c) 8.7 ohms.
 * d) 10 ohms.
 * e) 11.5 ohms.

70) Two 9.4 ohm resistors are connected in parallel.  This combination is then connected in series to a 2.4 ohm resistor.  What is the net resistance?
 * a) 5.4 ohms.
 * b) 6.2 ohms.
 * c) 7.1 ohms.
 * d) 8.2 ohms.
 * e) 9.4 ohms.

71) An ideal 7.5 volt battery is connected to a 0.084 ohm resistor.  To measure the current an ammeter with a resistance of 14$$m\Omega$$ is used.  What current does the ammeter actually read?
 * a) 43.8 A.
 * b) 50.3 A.
 * c) 57.9 A.
 * d) 66.5 A.
 * e) 76.5 A.

72) A battery has an emf of 7 volts, and an internal resistance of 357 $$k\Omega$$. It is connected to a 2.9 $$M\Omega$$ resistor.  What power is developed in the 2.9  $$M\Omega$$ resistor?
 * a) 13.4 $$\mu$$W.
 * b) 15.4 $$\mu$$W.
 * c) 17.72 $$\mu$$W.
 * d) 20.37 $$\mu$$W.
 * e) 23.43 $$\mu$$W.

73) A 819 mF capacitor is connected in series to a 798 k&Omega; resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)
 * a) 8.27 x 105 s.
 * b) 2.61 x 106 s.
 * c) 8.27 x 106 s.
 * d) 2.61 x 107 s.
 * e) 8.27 x 107 s.

74) A 65 &mu;F capacitor is connected in series to a 414 k&Omega; resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)
 * a) 1.08 x 101 s.
 * b) 3.4 x 101 s.
 * c) 1.08 x 102 s.
 * d) 3.4 x 102 s.
 * e) 1.08 x 103 s.

75) A 727 mF capacitor is connected in series to a 860 M&Omega; resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)
 * a) 1.88 x 109 s.
 * b) 5.93 x 109 s.
 * c) 1.88 x 1010 s.
 * d) 5.93 x 1010 s.
 * e) 1.88 x 1011 s.

76) A 10 F capacitor is connected in series to a 10&Omega; resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)
 * a) 4 x 100 s.
 * b) 1.26 x 101 s.
 * c) 4 x 101 s.
 * d) 1.26 x 102 s.
 * e) 4 x 102 s.

77) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?
 * a) 1.3 x 102 m.
 * b) 4.1 x 102 m.
 * c) 1.3 x 103 m.
 * d) 4.1 x 103 m.
 * e) 1.3 x 104 m.

78) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?
 * a) 2.36 x 10-3 newtons
 * b) 7.47 x 10-3 newtons
 * c) 2.36 x 10-2 newtons
 * d) 7.47 x 10-2 newtons
 * e) 2.36 x 10-1 newtons

79) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?
 * a) 5.14 x 10-5 Volts
 * b) 1.62 x 10-4 Volts
 * c) 5.14 x 10-4 Volts
 * d) 1.62 x 10-3 Volts
 * e) 5.14 x 10-3 Volts

80) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?
 * a) 1.1 x 100 volts
 * b) 3.6 x 100 volts
 * c) 1.1 x 101 volts
 * d) 3.6 x 101 volts
 * e) 1.1 x 102 volts

81) Two orbiting satellites are orbiting at a speed of 58 km/s perpendicular to a magnetic field of 46 &mu;T. They are connected by a cable that is 22 km long.  A voltmeter is attached between a satellite and one end of the cable.  The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit.  What is the measured voltage?
 * a) 2.72 x 104 volts.
 * b) 3.3 x 104 volts.
 * c) 4 x 104 volts.
 * d) 4.84 x 104 volts.
 * e) 5.87 x 104 volts.

82) An loop of wire with 54 turns has a radius of 0.8 meters, and is oriented with its axis parallel to a magetic field of 0.86 Tesla. What is the induced voltage if this field is reduced to  46% of its original value in 2.4 seconds?
 * a) 1.43 x 101 volts
 * b) 1.73 x 101 volts
 * c) 2.1 x 101 volts
 * d) 2.55 x 101 volts
 * e) 3.08 x 101 volts

83) Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
 * a) how a nearsighted person might see a distant object
 * b) how a farsighted person might see an object that is too close for comfort
 * c) how a nearsighted person might see an object that is too close for comfort
 * d) how a farsighted person might see a distant object

84)  Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
 * a) how a farsighted person might see a distant object
 * b) how a nearsighted person might see an object that is too close for comfort
 * c) how a farsighted person might see an object that is too close for comfort
 * d) how a nearsighted person might see a distant object

85) In optics, normal means
 * a) parallel to the surface
 * b) to the right of the optical axis
 * c) to the left of the optical axis
 * d) perpendicular to the surface

86) The law of reflection applies to
 * a) only light in a vacuum
 * b) flat surfaces
 * c) telescopes but not microscopes
 * d) curved surfaces
 * e) both flat and curved surfaces

87) When light passes from air to glass
 * a) the frequency decreases
 * b) the frequency increases
 * c) it bends away from the normal
 * d) it does not bend
 * e) it bends towards the normal

88) When light passes from glass to air
 * a) the frequency increases
 * b) it bends towards the normal
 * c) the frequency decreases
 * d) it does not bend
 * e) it bends away from the normal

89) An important principle that allows fiber optics to work is
 * a) total external refraction
 * b) the Doppler shift
 * c) partial internal absorption
 * d) the invariance of the speed of light
 * e) total internal reflection

90) The focal point is where
 * a) the center of the lens
 * b) rays meet whenever they are forming an image
 * c) rays meet whenever they pass through a lens
 * d) rays meet if they are parallel to each other
 * e) rays meet if they were parallel to the optical axis before striking a lens

91) An object is placed 8.6 cm to the left of a diverging lens with a focal length of 6.3 cm. How far is the image from the lens?
 * a) 3.64 x 10-1 cm
 * b) 6.47 x 10-1 cm
 * c) 1.15 x 100 cm
 * d) 2.04 x 100 cm
 * e) 3.64 x 100 cm

92) An object is placed 6.55 cm to the left of a converging lens with a focal length of 5.4 cm. How far is the image from the lens?
 * a) 3.08 x 100 cm
 * b) 5.47 x 100 cm
 * c) 9.73 x 100 cm
 * d) 1.73 x 101 cm
 * e) 3.08 x 101 cm

93) An object of height 0.67 cm is placed 107 cm behind a diverging lens with a focal length of 70 cm. What is the height of the image?
 * a) 2.65 x 10-1 cm
 * b) 3.18 x 10-1 cm
 * c) 3.82 x 10-1 cm
 * d) 4.58 x 10-1 cm
 * e) 5.49 x 10-1 cm

94) An object is placed 10.8 cm to the left of a diverging lens with a focal length of 15.6 cm. On the side, at a distance of 5.7 cm from the diverging lens is a converging lens with focal length equal to 4 cm.  How far is the final image from the converging lens?
 * a) 5.98 x 10-1 cm
 * b) 1.89 x 100 cm
 * c) 5.98 x 100 cm
 * d) 1.89 x 101 cm
 * e) 5.98 x 101 cm

95) Which lens has the shorter focal length?
 * a) Ray_drawing_eye_schematic.svg
 * b) Ray drawing eye schematic01.svg
 * c) They have the same focal lengh.

96) If this represents the eye looking at an object, where is this object?
 * a) very far away
 * b) One focal length in front of the eye
 * c) at infinity
 * d) directly in front of the eye (almost touching)
 * e) Two (of the other answers) are true

97) After passing through a the lens of a camera or the eye, the focal point is defined as where the rays meet.
 * a) true
 * b) false

98) Mr. Smith is gazing at something as shown in the figure to the left.  Suppose he does not refocus, but attempts to stare at the star shown in the figures below.  Which diagram depicts how the rays from the star would travel if he does not refocus?
 * a) Ray drawing eye schematic02.svg
 * b) Ray drawing eye Wrong Answer.svg
 * c) Ray_drawing_eye_schematic_alternate.svg

99) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 7.3A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 8.3m.
 * a) 4.76E+01 m
 * b) 5.22E+01 m
 * c) 5.72E+01 m
 * d) 6.27E+01 m
 * e) 6.87E+01 m

100) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 8.8m from a wire carrying a current of 8.6A?
 * a) 1.56E-01 A/m
 * b) 1.71E-01 A/m
 * c) 1.87E-01 A/m
 * d) 2.05E-01 A/m
 * e) 2.25E-01 A/m

101) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (8.407,2.6006) if a current of 8.6A flows through a wire that runs along the z axis?
 * a) 1.13E-01 A/m
 * b) 1.24E-01 A/m
 * c) 1.36E-01 A/m
 * d) 1.49E-01 A/m
 * e) 1.63E-01 A/m

102) A very long and thin solenoid has 1982 turns and is 154 meters long. The wire carrys a current of 9.1A. What is the magnetic field in the center?
 * a) 1.12E-04 Tesla
 * b) 1.22E-04 Tesla
 * c) 1.34E-04 Tesla
 * d) 1.47E-04 Tesla
 * e) 1.61E-04 Tesla

103) A very long and thin solenoid has 1965 turns and is 136 meters long. The wire carrys a current of 7.6A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 43 meters from the center and stops 88 meters from the center?
 * a) 2.75E+03 A
 * b) 3.01E+03 A
 * c) 3.30E+03 A
 * d) 3.62E+03 A
 * e) 3.97E+03 A

104) What is the sum of 0.2 apples plus 57 apples?
 * a) 5.72E+01 apples
 * b) 6.27E+01 apples
 * c) 6.88E+01 apples
 * d) 7.54E+01 apples
 * e) 8.27E+01 apples

105) H is defined by, B=&mu;0H, where B is magnetic field. A current of 54A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,5.4) to the point (5.4,0).
 * a) 9.34E+00 amps
 * b) 1.02E+01 amps
 * c) 1.12E+01 amps
 * d) 1.23E+01 amps
 * e) 1.35E+01 amps

106) H is defined by, B=&mu;0H, where B is magnetic field. A current of 33A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.6, 6.6) to the point (6.6, 6.6).
 * a) 5.71E+00 amps
 * b) 6.26E+00 amps
 * c) 6.86E+00 amps
 * d) 7.52E+00 amps
 * e) 8.25E+00 amps

107) H is defined by, B=&mu;0H, where B is magnetic field. A current of 49A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,9.8) to the point (9.8,9.8).
 * a) 6.13E+00 amps
 * b) 6.72E+00 amps
 * c) 7.36E+00 amps
 * d) 8.07E+00 amps
 * e) 8.85E+00 amps

108) H is defined by, B=&mu;0H, where B is magnetic field. A current of 88A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,8.7) to (+ &infin; ,8.7).
 * a) 4.01E+01 amps
 * b) 4.40E+01 amps
 * c) 4.82E+01 amps
 * d) 5.29E+01 amps
 * e) 5.80E+01 amps

109) A circlular capactitor of radius 4.2 m has a gap of 12 mm, and a charge of 94 &mu;C.  What is the electric field between the plates?
 * a) 1.92E+05 N/C (or V/m)
 * b) 2.32E+05 N/C (or V/m)
 * c) 2.81E+05 N/C (or V/m)
 * d) 3.41E+05 N/C (or V/m)
 * e) 4.13E+05 N/C (or V/m)

110) A circlular capactitor of radius 4.3 m has a gap of 14 mm, and a charge of 15 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.
 * a) 8.75E-12 Vs2m-1
 * b) 1.06E-11 Vs2m-1
 * c) 1.28E-11 Vs2m-1
 * d) 1.56E-11 Vs2m-1
 * e) 1.88E-11 Vs2m-1

111) A circlular capactitor of radius 3.3 m has a gap of 12 mm, and a charge of 63 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is the decay time?
 * a) 9.94E-05 s
 * b) 1.20E-04 s
 * c) 1.46E-04 s
 * d) 1.77E-04 s
 * e) 2.14E-04 s

112) A circlular capactitor of radius 4.3 m has a gap of 10 mm, and a charge of 46 &mu;C.  The capacitor is discharged through a  5 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)
 * a) 8.32E-09 Tesla
 * b) 1.05E-08 Tesla
 * c) 1.32E-08 Tesla
 * d) 1.66E-08 Tesla
 * e) 2.09E-08 Tesla

S_G (key)
1) The temperature is -1.4 degrees Celsius, and you are standing 0.94 km from a cliff. What is the echo time?
 * -a) 4.883 x 100 seconds
 * -b) 5.272 x 100 seconds
 * +c) 5.693 x 100 seconds
 * -d) 6.147 x 100 seconds
 * -e) 6.637 x 100 seconds

2) While standing 0.77 km from a cliff, you measure the echo time to be 4.442 seconds. What is the temperature?
 * -a) 1.48 x 101Celsius
 * -b) 1.71 x 101Celsius
 * -c) 1.98 x 101Celsius
 * -d) 2.28 x 101Celsius
 * +e) 2.63 x 101Celsius

3) What is the speed of a transverse wave on a string if the string is 0.58 m long, clamped at both ends, and harmonic number 4 has a frequency of 543 Hz?
 * -a) 8.86 x 101 unit
 * -b) 1.07 x 102 unit
 * -c) 1.3 x 102 unit
 * +d) 1.57 x 102 unit
 * -e) 1.91 x 102 unit

4) Integrate the line integral of, $$\vec F = 7.3xy\hat x + 5.2y^3\hat y $$, along the y axis from  y = 5 to y = 11
 * + a) 1.82E+04
 * - b) 1.95E+04
 * - c) 2.09E+04
 * - d) 2.23E+04
 * - e) 2.39E+04

5) Integrate the function, $$\vec F = r^7\theta^8\hat r + r^9\theta^ 4\hat \theta$$, along the first quadrant of a circle of radius 8
 * - a) 1.68E+09
 * - b) 1.79E+09
 * - c) 1.92E+09
 * + d) 2.05E+09
 * - e) 2.20E+09

6) Integrate the line integral of $$\vec F = 4xy\hat x + 9.8x\hat y $$  from the origin to the point at x = 2.6 and y = 3.9
 * - a) 7.93E+01
 * + b) 8.48E+01
 * - c) 9.08E+01
 * - d) 9.71E+01
 * - e) 1.04E+02

7) Integrate the function, $$\vec F = -x^3y^5\hat x + x^2y^3\hat y$$, as a line integral around a unit square with corners at (0,0),(1,0),(1,1),(0,1). Orient the path so its direction is out of the paper by the right hand rule
 * - a) 3.81E-01
 * - b) 4.08E-01
 * - c) 4.37E-01
 * - d) 4.67E-01
 * + e) 5.00E-01

8) What is the magnitude of the electric field at the origin if a 1.8 nC charge is placed at x = 9.6 m, and a 2 nC charge is placed at y = 8.7 m?
 * +a) 2.95 x 10-1N/C
 * -b) 3.41 x 10-1N/C
 * -c) 3.94 x 10-1N/C
 * -d) 4.55 x 10-1N/C
 * -e) 5.25 x 10-1N/C

9) What angle does the electric field at the origin make with the x-axis if a 1.4 nC charge is placed at x = -8.7 m, and a 2.7  nC charge is placed at y = -8.3 m?
 * -a) 4.85 x 101degrees
 * -b) 5.61 x 101degrees
 * +c) 6.47 x 101degrees
 * -d) 7.48 x 101degrees
 * -e) 8.63 x 101degrees

10) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the x component of the electric field at  (x,y) =( 6a, 5a) is &beta;kQ/a2, where &beta; equals
 * -a) 1.09 x 10-3 unit
 * -b) 1.33 x 10-3 unit
 * +c) 1.61 x 10-3 unit
 * -d) 1.95 x 10-3 unit
 * -e) 2.36 x 10-3 unit

11) A dipole at the origin consists of charge Q placed at x = 0.5a, and charge of -Q placed at x = -0.5a. The absolute value of the y component of the electric field at  (x,y) =( 1.1a, 1.2a) is &beta;kQ/a2, where &beta; equals
 * -a) 1.61 x 10-1 unit
 * -b) 1.95 x 10-1 unit
 * -c) 2.36 x 10-1 unit
 * -d) 2.86 x 10-1 unit
 * +e) 3.47 x 10-1 unit

12) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal B=$$
 * -a) 3
 * -b) &minus;7
 * -c) &minus;3
 * -d) &minus;3
 * +e) 2

13) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) 5&minus;s
 * -b) s&minus;4
 * +c) 1&minus;s
 * -d) s&minus;1
 * -e) 5

14) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the y component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal F=$$:
 * +a) 3/2
 * -b) 1/2
 * -c) 2
 * -d) 2/3
 * -e) 3

15) A line of charge density &lambda; situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) 3&minus;s
 * -b) 8
 * -c) s&minus;3
 * +d) 7&minus;s
 * -e) s&minus;7

16) A line of charge density &lambda; situated on the x axis extends from x = 3 to x = 7. What is the x component of the electric field at the point (7, 8)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:
 * -a) 72 + 82
 * -b) 32 + 82
 * +c) (7-s)2 + 82
 * -d) 72 + (3&minus;s)2
 * -e) 72 + (8&minus;s)2

17) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$
 * -a) s&minus;3
 * -b) 3
 * -c) s&minus;7
 * -d) 3&minus;s
 * +e) 7&minus;s

18) A line of charge density &lambda; situated on the y axis extends from y = -3 to y = 2. What is the y component of the electric field at the point (3, 7)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where$$\mathcal F=$$
 * -a) 2
 * -b) 3
 * +c) 3/2
 * -d) 1/2

19) A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) 2
 * -b) s &minus; 9
 * -c) 2 &minus; s
 * -d) s &minus; 2
 * +e) 9 &minus; s

20) A line of charge density &lambda; situated on the y axis extends from y = 2 to y = 7. What is the y component of the electric field at the point (2, 9)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal D^2 + \mathcal E^2=$$:
 * -a) 92 + (2-s)2
 * +b) 22 + (9-s)2
 * -c) 22 + (7-s)2
 * -d) 92 + (7-s)2
 * -e) 72 + (2-s)2

21) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal A=$$:
 * +a) 4
 * -b) 2
 * -c) 1/2
 * -d) 8

22) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the y component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) s&minus;4
 * -b) 4&minus;s
 * -c) 8&minus;s
 * -d) s&minus;8
 * +e) 4

23) A line of charge density &lambda; situated on the x axis extends from x = 4 to x = 8. What is the x component of the electric field at the point (8, 4)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * +a) 8&minus;s
 * -b) 4&minus;s
 * -c) s&minus;8
 * -d) s&minus;4
 * -e) 4

24) A line of charge density &lambda; situated on the y axis extends from y = 4 to y = 6. What is the x component of the electric field at the point (5, 1)? $$Answer$$ (assuming $$\mathcal B > \mathcal A$$) $$ is: \frac{1}{4\pi\epsilon_0}\int_\mathcal A^\mathcal B\frac{ \mathcal C\;\lambda ds}{\left[\mathcal D^2+\mathcal E^2\right]^\mathcal F\;}$$, where $$\mathcal C=$$:
 * -a) s&minus;1
 * -b) 5&minus;s
 * -c) s&minus;4
 * +d) 5
 * -e) 1&minus;s

25) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. The height is much less than the radius: H << R. The electric field at the center vanishes.  What formula describes the electric field at a distance, z, on axis from the center if z > H/2?
 * -a)c) $$\varepsilon_0 E=  H\rho z$$
 * +b)e) $$\varepsilon_0 E = H\rho /2$$
 * -c)d) none of these are correct
 * -d) $$\varepsilon_0 E=   \rho z $$
 * -e)b) $$\varepsilon_0 E=  H\rho $$

26) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. The height is much less than the radius: H << R. The electric field at the center vanishes.  What formula describes the electric field at a distance, z, on axis from the center if z < H/2?
 * +a)c) $$\varepsilon_0 E=   \rho z $$
 * -b) $$\varepsilon_0 E = H\rho /2$$
 * -c)e) $$\varepsilon_0 E=  H\rho z$$
 * -d)d) $$\varepsilon_0 E=  H\rho $$
 * -e)b) none of these are correct

27) A sphere has a uniform charge density of $$\rho$$, and a radius or R. What formula describes the electric field at a distance r > R?
 * -a)d) $$ r^2\varepsilon_0 E=r^3\rho /2$$
 * -b) none of these are correct
 * -c)b) $$ r^2\varepsilon_0 E=R^3\rho /2$$
 * -d)c) $$ r^2\varepsilon_0 E= r^3\rho/3$$
 * +e)e) $$ r^2\varepsilon_0 E=R^3\rho /3$$

28) A sphere has a uniform charge density of $$\rho$$, and a radius equal to R. What formula describes the electric field at a distance r < R?
 * +a)d) $$ r^2\varepsilon_0 E=r^3\rho /3$$
 * -b)b) $$ r^2\varepsilon_0 E=R^3\rho /3$$
 * -c) $$ r^2\varepsilon_0 E=r^3\rho /2$$
 * -d)e) $$ r^2\varepsilon_0 E=R^3\rho /2$$
 * -e)c) none of these are correct

29) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. The height is much greater than the radius: H >> R. The electric field at the center vanishes.  What formula describes the electric field at a distance, r, radially from the center if r < R?
 * +a)c) $$2\varepsilon_0 E = r\rho $$
 * -b) $$2R\varepsilon_0 E=  r^2\rho $$
 * -c)e) $$2r^2\varepsilon_0 E= R^3  \rho $$
 * -d)b) $$2r\varepsilon_0 E = R^2\rho $$
 * -e)d) none of these are correct

30) A cylinder of radius, R, and height H has a uniform charge density of $$\rho$$. The height is much greater than the radius: H >> R. The electric field at the center vanishes.  What formula describes the electric field at a distance, r, radially from the center if r > R?
 * -a)e) $$2r^2\varepsilon_0 E= R^3  \rho $$
 * -b)d) none of these are correct
 * -c) $$2R\varepsilon_0 E=  r^2\rho $$
 * +d)c) $$2r\varepsilon_0 E = R^2\rho $$
 * -e)b) $$2\varepsilon_0 E = r\rho $$

31) A parallel plate capacitor has both plates with an area of 1.45 m2. The separation between the plates is  1.53mm.  Applied to the plates is a potential difference of 2.55 kV.  What is the capacitance?
 * +a) 8.39 nF.
 * -b) 9.65 nF.
 * -c) 11.1 nF.
 * -d) 12.76 nF.
 * -e) 14.68 nF.

32) The same parallel plate capacitor, with area 1.45 m2, plate separation  1.53mm, and an applied voltage of 2.55 kV.  How much charge is stored?
 * -a) 12.23 &mu;C.
 * -b) 14.07 &mu;C.
 * -c) 16.18 &mu;C.
 * -d) 18.61 &mu;C.
 * +e) 21.4 &mu;C.

33) A 0.5 Farad capacitor is charged with 1.6 Coulombs. What is the value of the electric field if the plates are 0.7 mm apart?
 * -a) 3.46 kV/m.
 * -b) 3.98 kV/m.
 * +c) 4.57 kV/m.
 * -d) 5.26 kV/m.
 * -e) 6.05 kV/m.

34) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the energy stored in the capacitor if the plates are 0.7 mm apart?
 * -a) 1.28 J.
 * -b) 1.47 J.
 * +c) 1.69 J.
 * -d) 1.94 J.
 * -e) 2.24 J.

35) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the force between the plates if they are 0.3 mm apart?
 * -a) 4025 N.
 * +b) 4628 N.
 * -c) 5322 N.
 * -d) 6121 N.
 * -e) 7039 N.

36) How fast is a 2663 eV electron moving?
 * +a) 3.1 x 107 m/s.
 * -b) 4.6 x 107 m/s.
 * -c) 6.9 x 107 m/s.
 * -d) 1 x 108 m/s.
 * -e) 1.5 x 108 m/s.

37) A proton is accellerated (at rest) from a plate held at 39.7 volts to a plate at zero volts. What is the final speed?
 * -a) 3.9 x 104 m/s.
 * -b) 5.8 x 104 m/s.
 * +c) 8.7 x 104 m/s.
 * -d) 1.3 x 105 m/s.
 * -e) 2 x 105 m/s.

38) What voltage is required accelerate an electron at rest to a speed of 3 x 105 m/s?
 * -a) 1.7 x 10-1 volts
 * +b) 2.6 x 10-1 volts
 * -c) 3.8 x 10-1 volts
 * -d) 5.8 x 10-1 volts
 * -e) 8.6 x 10-1 volts

39) What voltage is required to stop a proton moving at a speed of 1.6 x 104 m/s?
 * -a) 4 x 10-1 volts
 * -b) 5.9 x 10-1 volts
 * -c) 8.9 x 10-1 volts
 * +d) 1.3 x 100 volts
 * -e) 2 x 100 volts

40) A cylinder of radius, r=3, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,  $$\vec\mathfrak F = (2.12+1.68z)\rho^2\hat\rho +8.83z^3\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the top surface of the cylinder.
 * -a) 4.593E+03
 * -b) 5.564E+03
 * +c) 6.741E+03
 * -d) 8.167E+03
 * -e) 9.894E+03

41) A cylinder of radius, r=2, and height, h=6, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,  $$\vec\mathfrak F = (1.86+2.43z)\rho^2\hat\rho +9.75z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\int_{side}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the curved side surface of the cylinder.
 * +a) 5.610E+02
 * -b) 6.796E+02
 * -c) 8.234E+02
 * -d) 9.975E+02
 * -e) 1.209E+03

42) A cylinder of radius, r=2, and height, h=4, is centered at the origin and oriented along the z axis. A vector field can be expressed in cylindrical coordinates as,  $$\vec\mathfrak F = (2.14+2.8z)\rho^2\hat\rho +9.94z^2\hat z $$ Let $$\hat n$$ be the outward unit normal to this cylinder and evaluate, $$\left |\oint\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the entire surface of the cylinder.
 * -a) 2.93E+02
 * -b) 3.55E+02
 * +c) 4.30E+02
 * -d) 5.21E+02
 * -e) 6.32E+02

43) A 5.1 volt battery moves 43 Coulombs of charge in 1.5 hours. What is the power?
 * +a) 4.06 x 10-2 W
 * -b) 4.92 x 10-2 W
 * -c) 5.96 x 10-2 W
 * -d) 7.22 x 10-2 W
 * -e) 8.75 x 10-2 W

44) The diameter of a copper wire is 8.3 mm, and it carries a current of 87 amps. What is the drift velocity if copper has a density of 8.8E3 kg/m3 and an atomic mass of 63.54 g/mol? (1 mol = 6.02E23 atoms, and copper has one free electron per atom.)
 * -a) 6.77 x 10-5m/s
 * -b) 8.2 x 10-5m/s
 * -c) 9.93 x 10-5m/s
 * +d) 1.2 x 10-4m/s
 * -e) 1.46 x 10-4m/s

45) A 196 Watt DC motor draws 0.35 amps of current. What is effective resistance?
 * +a) 1.6 x 103 &Omega;
 * -b) 1.94 x 103 &Omega;
 * -c) 2.35 x 103 &Omega;
 * -d) 2.85 x 103 &Omega;
 * -e) 3.45 x 103 &Omega;

46) A power supply delivers 101 watts of power to a 219 ohm resistor.  What was the applied voltage?
 * +a) 1.49 x 102 volts
 * -b) 1.8 x 102 volts
 * -c) 2.18 x 102 volts
 * -d) 2.64 x 102 volts
 * -e) 3.2 x 102 volts

47) 3 amps flow through a 1 Ohm resistor. What is the voltage?}
 * -a) None these are correct.
 * +b) $$3V$$
 * -c) $$1V$$
 * -d) $$\frac{1}{3}V$$

48) A 1 ohm resistor has 5 volts DC across its terminals. What is the current (I) and the power consumed?}
 * -a) I = 5A &  P = 5W.
 * -b) I = 5A &  P = 3W.
 * +c) I = 5A &  P = 25W.
 * -d) I = 5A &  P = 9W

49) The voltage across two resistors in series is 10 volts. One resistor is twice as large as the other. What is the voltage across the larger resistor? What is the voltage across the smaller one? }
 * -a) $$V_{small-Resistor} = 5V$$ and $$V_{Big-Resistor} = 5V$$.
 * +b) $$V_{Big-Resistor} = 6.67V$$ and $$V_{small-Resistor} = 3.33V$$.
 * -c) None of these are true.
 * -d) $$V_{Big-Resistor} = 3.33V$$ and$$V_{small-Resistor} = 6.67V$$.

50) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in series. What is the total resistance?}
 * +a) $$R_{Total} = 6\Omega$$.
 * -b) $$R_{Total} = 3\Omega$$.
 * -c) $$R_{Total} = 0.5454\Omega$$.
 * -d) None of these are true.

51) Two identical resistors are connected in series. The voltage across both of them is 250 volts. What is the voltage across each one?}
 * -a) $$R_1 = 250V$$ and $$R_2 = 0V$$.
 * -b) $$R_1 = 150V$$ and $$R_2 = 100V$$.
 * +c) $$R_1 = 125V$$ and $$R_2 = 125V$$.
 * -d) None of these are true.

52) A 1 ohm, 2 ohm, and 3 ohm resistor are connected in parallel. What is the total resistance?}
 * -a) $$\frac{11}{6}\Omega$$.
 * -b) $$\frac{6}{3}\Omega$$.
 * +c) $$\frac{6}{11}\Omega$$.
 * -d) $$\frac{3}{6}\Omega$$.

53) A 5 ohm and a 2 ohm resistor are connected in parallel. What is the total resistance?}
 * -a) $$\frac{7}{10}\Omega$$.
 * -b)  $$\frac{6}{10}\Omega$$.
 * -c) $$\frac{10}{6}\Omega$$.
 * +d) $$\frac{10}{7}\Omega$$.

54) A 7 ohm and a 3 ohm resistor are connected in parallel. What is the total resistance?}
 * +a) $$\frac{21}{10}\Omega$$.
 * -b) $$\frac{10}{21}\Omega$$.
 * -c) $$\frac{7}{11}\Omega$$.
 * -d) $$\frac{11}{7}\Omega$$.

55) Three 1 ohm resistors are connected in parallel. What is the total resistance?}
 * -a) $$ 3\Omega$$.
 * -b) $$\frac{2}{3}\Omega$$.
 * -c) $$\frac{3}{2}\Omega$$.
 * +d) $$\frac{1}{3}\Omega$$.

56) If you put an infinite number of resistors in parallel, what would the total resistance be?}
 * -a) $$R_{total}$$ would approach 1 as The No. of Resistors In parallel Approaches Infinity
 * -b) It is not possible to connect that Number of Resistors in parallel.
 * -c)  None of these are true.
 * +d)  $$R_{total}$$ would approach Zero as The No. of Resistors In parallel Approaches Infinity.

57) What is the current through R1 and R2 in the figure shown?
 * -a)  $$I_1 = 0.1A$$ and $$I_2 = 0.1667A$$.
 * -b)  $$I_1 = 10A$$ and $$I_2 = 16.67A$$.
 * +c)  $$I_1 = 1A$$ and $$I_2 = 1.667A$$.
 * -d) $$I_1 = 1A$$ and $$I_2 = 25A$$.

58) Why do we say the "voltage across" or "the voltage with respect to?" Why can't we just say voltage?}
 * -a) The other point could be Negative or positive.
 * -b) It's an Electrical Cliche.
 * -c) None these are correct
 * +d) Voltage is a measure of Electric Potential difference between two electrical points.

59) What is the current through R1, R2, R3, and R4 in the figure shown?
 * +a) $$I_1 = 1A$$; $$I_2 = 0.5A$$; $$I_3 = 0.33A$$; $$I_4 = 0.25A$$.
 * -b)  $$I_1 = 10A$$; $$I_2 = 50A$$; $$I_3 = 33A$$; $$I_4 = 25A$$..
 * -c) $$I_1 = 0.25A$$; $$I_2 = 0.33A$$; $$I_3 = 0.5A$$; $$I_4 = 0.1A$$.
 * -d) $$I_1 = 1A$$; $$I_2 = 5A$$; $$I_3 = 3.3A$$; $$I_4 = 2.5A$$.

60) Two resistors are in parallel with a voltage source. How do their voltages compare?}
 * -a) The voltage across both resistors is half the voltage of the source.
 * -b) None of these are true.
 * -c) One has full voltage, the other has none.
 * +d) The voltage across both resistors is the same as the source.

61) A resistor consumes 5 watts, and its current is 10 amps. What is its voltage?
 * -a) 10V.
 * +b) 0.5V.
 * -c) 2V.
 * -d) 15V.

62) A resistor has 10 volts across it and 4 amps going through it. What is its resistance?}
 * -a) None of these are true.
 * -b) $$3.5\Omega.$$
 * +c) $$2.5\Omega.$$
 * -d) $$4.5\Omega.$$

63) If you plot voltage vs. current in a circuit, and you get a linear line, what is the significance of the slope? }
 * -a) None of these are true.
 * +b) Resistance.
 * -c) Discriminant.
 * -d) Power.

64) A resistor has 3 volts across it. Its resistance is 1.5 ohms. What is the current?}
 * -a) 12A
 * +b) 2A
 * -c) 3A
 * -d) 1.5A

65) A resistor has 8 volts across it and 3 Amps going through it. What is the power consumed?}
 * +a) 24W
 * -b) 8W
 * -c) 2.2W
 * -d) 3W

66) A resistor has a voltage of 5 volts and a resistance of 15 ohms. What is the power consumed? }
 * +a) 1.67 Watts
 * -b) None of these are ture.
 * -c) 2.5 Watts
 * -d) 11.67 Joules

67) A resistor is on for 5 seconds. It consumes power at a rate of 5 watts. How many joules are used?}
 * -a) 3 Joules
 * -b) None of these are true
 * -c) 5 Joules
 * +d) 25 Joules

68) An ideal 4.2 V voltage source is connected to two resistors in parallel.  One is 1.6$$k\Omega$$, and the other is 2.1 $$k\Omega$$.  What is the current through the larger resistor?
 * -a) 0.75 mA.
 * -b) 0.86 mA.
 * -c) 0.99 mA.
 * +d) 1.14 mA.
 * -e) 1.31 mA.

69) A 6.6 ohm resistor is connected in series to a pair of 6.4 ohm resistors that are in parallel.  What is the net resistance?
 * -a) 6.4 ohms.
 * -b) 7.4 ohms.
 * -c) 8.5 ohms.
 * +d) 9.8 ohms.
 * -e) 11.3 ohms.

70) Two 6.2 ohm resistors are connected in parallel.  This combination is then connected in series to a 2.4 ohm resistor.  What is the net resistance?
 * -a) 3.1 ohms.
 * -b) 3.6 ohms.
 * -c) 4.2 ohms.
 * -d) 4.8 ohms.
 * +e) 5.5 ohms.

71) An ideal 6.8 volt battery is connected to a 0.096 ohm resistor.  To measure the current an ammeter with a resistance of 29$$m\Omega$$ is used.  What current does the ammeter actually read?
 * -a) 35.8 A.
 * -b) 41.1 A.
 * -c) 47.3 A.
 * +d) 54.4 A.
 * -e) 62.6 A.

72) A battery has an emf of 5.6 volts, and an internal resistance of 460 $$k\Omega$$. It is connected to a 2.4 $$M\Omega$$ resistor.  What power is developed in the 2.4  $$M\Omega$$ resistor?
 * -a) 6.05 $$\mu$$W.
 * -b) 6.96 $$\mu$$W.
 * -c) 8 $$\mu$$W.
 * +d) 9.2 $$\mu$$W.
 * -e) 10.58 $$\mu$$W.

73) A 819 mF capacitor is connected in series to a 798 k&Omega; resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)
 * -a) 8.27 x 105 s.
 * +b) 2.61 x 106 s.
 * -c) 8.27 x 106 s.
 * -d) 2.61 x 107 s.
 * -e) 8.27 x 107 s.

74) A 65 &mu;F capacitor is connected in series to a 414 k&Omega; resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)
 * -a) 1.08 x 101 s.
 * -b) 3.4 x 101 s.
 * +c) 1.08 x 102 s.
 * -d) 3.4 x 102 s.
 * -e) 1.08 x 103 s.

75) A 727 mF capacitor is connected in series to a 860 M&Omega; resistor. If the capacitor is discharged, how long does it take to fall by a factor of e3? (where e =2.7...)
 * +a) 1.88 x 109 s.
 * -b) 5.93 x 109 s.
 * -c) 1.88 x 1010 s.
 * -d) 5.93 x 1010 s.
 * -e) 1.88 x 1011 s.

76) A 10 F capacitor is connected in series to a 10&Omega; resistor. If the capacitor is discharged, how long does it take to fall by a factor of e4? (where e =2.7...)
 * -a) 4 x 100 s.
 * -b) 1.26 x 101 s.
 * -c) 4 x 101 s.
 * -d) 1.26 x 102 s.
 * +e) 4 x 102 s.

77) A cosmic ray alpha particle encounters Earth's magnetic field at right angles to a field of 7.4 &mu;T. The kinetic energy is 437 keV.  What is the radius of particle's orbit?
 * -a) 1.3 x 102 m.
 * -b) 4.1 x 102 m.
 * -c) 1.3 x 103 m.
 * -d) 4.1 x 103 m.
 * +e) 1.3 x 104 m.

78) Two parallel wires are 7.5 meters long, and are separated by 4.4 mm. What is the force if both wires carry a current of 14.8 amps?
 * -a) 2.36 x 10-3 newtons
 * -b) 7.47 x 10-3 newtons
 * -c) 2.36 x 10-2 newtons
 * +d) 7.47 x 10-2 newtons
 * -e) 2.36 x 10-1 newtons

79) Blood is flowing at an average rate of 24.5 cm/s in an artery that has an inner diameter of 3.9 mm.  What is the voltage across a hall probe placed across the inner diameter of the artery if the perpendicular magnetic field is 0.17 Tesla?
 * -a) 5.14 x 10-5 Volts
 * +b) 1.62 x 10-4 Volts
 * -c) 5.14 x 10-4 Volts
 * -d) 1.62 x 10-3 Volts
 * -e) 5.14 x 10-3 Volts

80) An electron tube on Earth's surface is oriented horizontally towards magnetic north. The electron is traveling at 0.06c, and Earth's magnetic field makes an angle of 48.5 degrees with respect to the horizontal.  To counter the magnetic force, a voltage is applied between two large parallel plates that are 59  mm apart.  What must be the applied voltage if the magnetic field is 45&mu;T?
 * -a) 1.1 x 100 volts
 * -b) 3.6 x 100 volts
 * -c) 1.1 x 101 volts
 * +d) 3.6 x 101 volts
 * -e) 1.1 x 102 volts

81) Two orbiting satellites are orbiting at a speed of 53 km/s perpendicular to a magnetic field of 58 &mu;T. They are connected by a cable that is 29 km long.  A voltmeter is attached between a satellite and one end of the cable.  The voltmeter's internal impedance far exceeds the net resistance through the ionosphere that completes the circuit.  What is the measured voltage?
 * -a) 7.36 x 104 volts.
 * +b) 8.91 x 104 volts.
 * -c) 1.08 x 105 volts.
 * -d) 1.31 x 105 volts.
 * -e) 1.59 x 105 volts.

82) An loop of wire with 31 turns has a radius of 0.9 meters, and is oriented with its axis parallel to a magetic field of 0.83 Tesla. What is the induced voltage if this field is reduced to  35% of its original value in 1.7 seconds?
 * -a) 2.07 x 101 volts
 * +b) 2.5 x 101 volts
 * -c) 3.03 x 101 volts
 * -d) 3.67 x 101 volts
 * -e) 4.45 x 101 volts

83) Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
 * -a) how a nearsighted person might see an object that is too close for comfort
 * -b) how a farsighted person might see an object that is too close for comfort
 * -c) how a farsighted person might see a distant object
 * +d) how a nearsighted person might see a distant object

84)  Shown is a corrective lens by a person who needs glasses. This ray diagram illustrates
 * -a) how a farsighted person might see a distant object
 * -b) how a nearsighted person might see a distant object
 * -c) how a nearsighted person might see an object that is too close for comfort
 * +d) how a farsighted person might see an object that is too close for comfort

85) In optics, normal means
 * -a) parallel to the surface
 * +b) perpendicular to the surface
 * -c) to the left of the optical axis
 * -d) to the right of the optical axis

86) The law of reflection applies to
 * -a) telescopes but not microscopes
 * -b) flat surfaces
 * -c) curved surfaces
 * +d) both flat and curved surfaces
 * -e) only light in a vacuum

87) When light passes from air to glass
 * -a) it does not bend
 * -b) the frequency increases
 * -c) the frequency decreases
 * -d) it bends away from the normal
 * +e) it bends towards the normal

88) When light passes from glass to air
 * -a) the frequency decreases
 * -b) the frequency increases
 * +c) it bends away from the normal
 * -d) it does not bend
 * -e) it bends towards the normal

89) An important principle that allows fiber optics to work is
 * -a) the invariance of the speed of light
 * -b) the Doppler shift
 * -c) partial internal absorption
 * +d) total internal reflection
 * -e) total external refraction

90) The focal point is where
 * +a) rays meet if they were parallel to the optical axis before striking a lens
 * -b) rays meet whenever they pass through a lens
 * -c) rays meet if they are parallel to each other
 * -d) the center of the lens
 * -e) rays meet whenever they are forming an image

91) An object is placed 3.5 cm to the left of a diverging lens with a focal length of 5.6 cm. How far is the image from the lens?
 * -a) 2.15 x 10-1 cm
 * -b) 3.83 x 10-1 cm
 * -c) 6.81 x 10-1 cm
 * -d) 1.21 x 100 cm
 * +e) 2.15 x 100 cm

92) An object is placed 4.35 cm to the left of a converging lens with a focal length of 5.7 cm. How far is the image from the lens?
 * -a) 1.03 x 101 cm
 * +b) 1.84 x 101 cm
 * -c) 3.27 x 101 cm
 * -d) 5.81 x 101 cm
 * -e) 1.03 x 102 cm

93) An object of height 0.75 cm is placed 147 cm behind a diverging lens with a focal length of 86 cm. What is the height of the image?
 * +a) 2.77 x 10-1 cm
 * -b) 3.32 x 10-1 cm
 * -c) 3.99 x 10-1 cm
 * -d) 4.78 x 10-1 cm
 * -e) 5.74 x 10-1 cm

94) An object is placed 10.2 cm to the left of a diverging lens with a focal length of 16.6 cm. On the side, at a distance of 5.6 cm from the diverging lens is a converging lens with focal length equal to 4 cm.  How far is the final image from the converging lens?
 * -a) 6.02 x 10-1 cm
 * -b) 1.9 x 100 cm
 * +c) 6.02 x 100 cm
 * -d) 1.9 x 101 cm
 * -e) 6.02 x 101 cm

95) Which lens has the shorter focal length?
 * -a) They have the same focal lengh.
 * +b) Ray_drawing_eye_schematic.svg
 * -c) Ray drawing eye schematic01.svg

96) If this represents the eye looking at an object, where is this object?
 * -a) at infinity
 * -b) One focal length in front of the eye
 * +c) Two (of the other answers) are true
 * -d) very far away
 * -e) directly in front of the eye (almost touching)

97) After passing through a the lens of a camera or the eye, the focal point is defined as where the rays meet.
 * +a) false
 * -b) true

98) Mr. Smith is gazing at something as shown in the figure to the left.  Suppose he does not refocus, but attempts to stare at the star shown in the figures below.  Which diagram depicts how the rays from the star would travel if he does not refocus?
 * -a) Ray_drawing_eye_schematic_alternate.svg
 * -b) Ray drawing eye Wrong Answer.svg
 * +c) Ray drawing eye schematic02.svg

99) Amphere's law for magnetostatic currents is that $$\oint\vec H\cdot\vec{d\ell}=\int\vec J\cdot \vec {dA}$$ equals the current enclosed by the closed loop, and $$B=\mu_0H$$ is the magnetic field. A current of 9.8A flows upward along the z axis. Noting that for this geometry, $$\oint \vec B \cdot\vec{d\ell} = B\oint d\ell$$, calculate the line integral $$\oint d\ell$$ for a circle of radius 4.6m.
 * +a) 2.89E+01 m
 * -b) 3.17E+01 m
 * -c) 3.47E+01 m
 * -d) 3.81E+01 m
 * -e) 4.18E+01 m

100) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H$$ at a distance of 8.2m from a wire carrying a current of 7.2A?
 * -a) 9.67E-02 A/m
 * -b) 1.06E-01 A/m
 * -c) 1.16E-01 A/m
 * -d) 1.27E-01 A/m
 * +e) 1.40E-01 A/m

101) If $$H=B/\mu_0$$, where $$B$$ is magnetic field, what is $$H_y$$ at the point (3.2194,2.9992) if a current of 5.8A flows through a wire that runs along the z axis?
 * -a) 1.06E-01 A/m
 * -b) 1.16E-01 A/m
 * -c) 1.28E-01 A/m
 * -d) 1.40E-01 A/m
 * +e) 1.54E-01 A/m

102) A very long and thin solenoid has 2979 turns and is 170 meters long. The wire carrys a current of 8.1A. What is the magnetic field in the center?
 * +a) 1.78E-04 Tesla
 * -b) 1.96E-04 Tesla
 * -c) 2.14E-04 Tesla
 * -d) 2.35E-04 Tesla
 * -e) 2.58E-04 Tesla

103) A very long and thin solenoid has 2240 turns and is 182 meters long. The wire carrys a current of 9.2A. If this solenoid is sufficiently thin, what is the line integral of$$\int \vec H\cdot\vec{d\ell}$$ along an on-axis path that starts 47 meters from the center and stops 109 meters from the center?
 * -a) 4.14E+03 A
 * -b) 4.54E+03 A
 * +c) 4.98E+03 A
 * -d) 5.46E+03 A
 * -e) 5.99E+03 A

104) What is the sum of 7.2 apples plus 9 apples?
 * +a) 1.62E+01 apples
 * -b) 1.78E+01 apples
 * -c) 1.95E+01 apples
 * -d) 2.14E+01 apples
 * -e) 2.34E+01 apples

105) H is defined by, B=&mu;0H, where B is magnetic field. A current of 40A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,6.7) to the point (6.7,0).
 * -a) 8.32E+00 amps
 * -b) 9.12E+00 amps
 * +c) 1.00E+01 amps
 * -d) 1.10E+01 amps
 * -e) 1.20E+01 amps

106) H is defined by, B=&mu;0H, where B is magnetic field. A current of 68A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point ( - 6.4, 6.4) to the point (6.4, 6.4).
 * -a) 1.55E+01 amps
 * +b) 1.70E+01 amps
 * -c) 1.86E+01 amps
 * -d) 2.04E+01 amps
 * -e) 2.24E+01 amps

107) H is defined by, B=&mu;0H, where B is magnetic field. A current of 89A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from the point (0,4.8) to the point (4.8,4.8).
 * -a) 9.25E+00 amps
 * -b) 1.01E+01 amps
 * +c) 1.11E+01 amps
 * -d) 1.22E+01 amps
 * -e) 1.34E+01 amps

108) H is defined by, B=&mu;0H, where B is magnetic field. A current of 74A passes along the z-axis. Use symmetry to find the integral, $$\int \vec H\cdot\vec{d\ell}$$, from  ( -&infin; ,9) to (+ &infin; ,9).
 * -a) 3.08E+01 amps
 * -b) 3.37E+01 amps
 * +c) 3.70E+01 amps
 * -d) 4.06E+01 amps
 * -e) 4.45E+01 amps

109) A circlular capactitor of radius 3.3 m has a gap of 14 mm, and a charge of 11 &mu;C.  What is the electric field between the plates?
 * -a) 2.04E+04 N/C (or V/m)
 * -b) 2.47E+04 N/C (or V/m)
 * -c) 3.00E+04 N/C (or V/m)
 * +d) 3.63E+04 N/C (or V/m)
 * -e) 4.40E+04 N/C (or V/m)

110) A circlular capactitor of radius 3.9 m has a gap of 19 mm, and a charge of 78 &mu;C.  Compute the surface integral  $$c^{-2}\oint\vec E\cdot d\vec A$$ over an inner face of the capacitor.
 * -a) 4.55E-11 Vs2m-1
 * -b) 5.51E-11 Vs2m-1
 * -c) 6.68E-11 Vs2m-1
 * -d) 8.09E-11 Vs2m-1
 * +e) 9.80E-11 Vs2m-1

111) A circlular capactitor of radius 4.7 m has a gap of 19 mm, and a charge of 27 &mu;C.  The capacitor is discharged through a  6 k&Omega; resistor.  What is the decay time?
 * -a) 1.60E-04 s
 * +b) 1.94E-04 s
 * -c) 2.35E-04 s
 * -d) 2.85E-04 s
 * -e) 3.45E-04 s

112) A circlular capactitor of radius 4.6 m has a gap of 12 mm, and a charge of 52 &mu;C.  The capacitor is discharged through a  7 k&Omega; resistor.  What is what is the maximum magnetic field at the edge of the capacitor? (There are two ways to do this; you should know both.)
 * -a) 3.30E-09 Tesla
 * -b) 4.15E-09 Tesla
 * -c) 5.23E-09 Tesla
 * +d) 6.58E-09 Tesla
 * -e) 8.29E-09 Tesla