OpenStax University Physics/Archived sample/T1V0

For instructor's eyes only Test 1 (of four tests plus the final).

PhysicsCalc2152657831440

PhysicsCalc2:T1:V0
PhysicsCalc2152657831440 1) Integrate the line integral of $$\vec F = 2xy\hat x + 7.2x\hat y $$  from the origin to the point at x = 2.4 and y = 3.2
 * a) 3.05E+01
 * b) 3.26E+01
 * c) 3.49E+01
 * d) 3.73E+01
 * e) 3.99E+01

2) 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, 3a) is &beta;kQ/a2, where &beta; equals
 * a) 3.38 x 10-3 unit
 * b) 4.1 x 10-3 unit
 * c) 4.96 x 10-3 unit
 * d) 6.01 x 10-3 unit
 * e) 7.28 x 10-3 unit

3) 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) 2.36 x 10-1 unit
 * b) 2.86 x 10-1 unit
 * c) 3.47 x 10-1 unit
 * d) 4.2 x 10-1 unit
 * e) 5.09 x 10-1 unit

4) 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) 7&minus;s
 * b) 3&minus;s
 * c) s&minus;7
 * d) 8
 * e) s&minus;3

5) 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) 1&minus;s
 * b) s&minus;4
 * c) 5
 * d) 5&minus;s
 * e) s&minus;1

6) 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) 2/3
 * b) 1/2
 * c) 2
 * d) 3
 * e) 3/2

7) A 1.4 Farad capacitor charged with 1.1 Coulombs. What is the force between the plates if they are 0.6 mm apart?
 * a) 412 N.
 * b) 474 N.
 * c) 545 N.
 * d) 626 N.
 * e) 720 N.

8) A 1.4 Farad capacitor charged with 1.1 Coulombs. What is the energy stored in the capacitor if the plates are 0.6 mm apart?
 * a) 0.38 J.
 * b) 0.43 J.
 * c) 0.5 J.
 * d) 0.57 J.
 * e) 0.66 J.

9) How fast is a 2952 eV electron moving?
 * a) 6.4 x 106 m/s.
 * b) 9.5 x 106 m/s.
 * c) 1.4 x 107 m/s.
 * d) 2.1 x 107 m/s.
 * e) 3.2 x 107 m/s.

10) A proton is accellerated (at rest) from a plate held at 729.8 volts to a plate at zero volts. What is the final speed?
 * a) 1.7 x 105 m/s.
 * b) 2.5 x 105 m/s.
 * c) 3.7 x 105 m/s.
 * d) 5.6 x 105 m/s.
 * e) 8.4 x 105 m/s.

11) 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, $$\vec\mathfrak F = (2.24+1.11z)\rho^3\hat\rho +8.16z^3\hat z $$ 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) 9.205E+02
 * b) 1.115E+03
 * c) 1.351E+03
 * d) 1.637E+03
 * e) 1.983E+03

12) 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, $$\vec\mathfrak F = (2.21+1.16z)\rho^2\hat\rho +7.96z^3\hat z $$ 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) 3.417E+03
 * b) 4.140E+03
 * c) 5.016E+03
 * d) 6.077E+03
 * e) 7.362E+03

KEY:PhysicsCalc2:T1:V0
PhysicsCalc2152657831440 1) Integrate the line integral of $$\vec F = 2xy\hat x + 7.2x\hat y $$  from the origin to the point at x = 2.4 and y = 3.2
 * -a) 3.05E+01
 * -b) 3.26E+01
 * -c) 3.49E+01
 * -d) 3.73E+01
 * +e) 3.99E+01

2) 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, 3a) is &beta;kQ/a2, where &beta; equals
 * -a) 3.38 x 10-3 unit
 * -b) 4.1 x 10-3 unit
 * -c) 4.96 x 10-3 unit
 * -d) 6.01 x 10-3 unit
 * +e) 7.28 x 10-3 unit

3) 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) 2.36 x 10-1 unit
 * -b) 2.86 x 10-1 unit
 * +c) 3.47 x 10-1 unit
 * -d) 4.2 x 10-1 unit
 * -e) 5.09 x 10-1 unit

4) 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) 7&minus;s
 * -b) 3&minus;s
 * -c) s&minus;7
 * -d) 8
 * -e) s&minus;3

5) 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) 1&minus;s
 * -b) s&minus;4
 * -c) 5
 * -d) 5&minus;s
 * -e) s&minus;1

6) 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) 2/3
 * -b) 1/2
 * -c) 2
 * -d) 3
 * +e) 3/2

7) A 1.4 Farad capacitor charged with 1.1 Coulombs. What is the force between the plates if they are 0.6 mm apart?
 * -a) 412 N.
 * -b) 474 N.
 * -c) 545 N.
 * -d) 626 N.
 * +e) 720 N.

8) A 1.4 Farad capacitor charged with 1.1 Coulombs. What is the energy stored in the capacitor if the plates are 0.6 mm apart?
 * -a) 0.38 J.
 * +b) 0.43 J.
 * -c) 0.5 J.
 * -d) 0.57 J.
 * -e) 0.66 J.

9) How fast is a 2952 eV electron moving?
 * -a) 6.4 x 106 m/s.
 * -b) 9.5 x 106 m/s.
 * -c) 1.4 x 107 m/s.
 * -d) 2.1 x 107 m/s.
 * +e) 3.2 x 107 m/s.

10) A proton is accellerated (at rest) from a plate held at 729.8 volts to a plate at zero volts. What is the final speed?
 * -a) 1.7 x 105 m/s.
 * -b) 2.5 x 105 m/s.
 * +c) 3.7 x 105 m/s.
 * -d) 5.6 x 105 m/s.
 * -e) 8.4 x 105 m/s.

11) 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, $$\vec\mathfrak F = (2.24+1.11z)\rho^3\hat\rho +8.16z^3\hat z $$ 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) 9.205E+02
 * -b) 1.115E+03
 * +c) 1.351E+03
 * -d) 1.637E+03
 * -e) 1.983E+03

12) 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, $$\vec\mathfrak F = (2.21+1.16z)\rho^2\hat\rho +7.96z^3\hat z $$ 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) 3.417E+03
 * -b) 4.140E+03
 * -c) 5.016E+03
 * +d) 6.077E+03
 * -e) 7.362E+03

KEY:PhysicsCalc2:T1:V1
PhysicsCalc2152657831440 1) 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, $$\vec\mathfrak F = (2+1.45z)\rho^2\hat\rho +8.02z^3\hat z $$ 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) 4.021E+02
 * -b) 4.872E+02
 * -c) 5.902E+02
 * -d) 7.151E+02
 * -e) 8.663E+02

2) A 0.5 Farad capacitor charged with 1.6 Coulombs. What is the energy stored in the capacitor if the plates are 0.7 mm apart?
 * -a) 2.23 J.
 * +b) 2.56 J.
 * -c) 2.94 J.
 * -d) 3.39 J.
 * -e) 3.89 J.

3) 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.

4) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the force between the plates if they are 0.7 mm apart?
 * -a) 1826 N.
 * -b) 2099 N.
 * +c) 2414 N.
 * -d) 2776 N.
 * -e) 3193 N.

5) 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) 2.86 x 10-1 unit
 * +b) 3.47 x 10-1 unit
 * -c) 4.2 x 10-1 unit
 * -d) 5.09 x 10-1 unit
 * -e) 6.17 x 10-1 unit

6) 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) 1/2
 * -b) 2
 * -c) 2/3
 * -d) 3
 * +e) 3/2

7) 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.

8) 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

9) 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, $$\vec\mathfrak F = (1.88+1.29z)\rho^2\hat\rho +7.2z^2\hat z $$ 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) 1.248E+03
 * -b) 1.512E+03
 * +c) 1.832E+03
 * -d) 2.220E+03
 * -e) 2.689E+03

10) 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;4
 * -b) 5&minus;s
 * -c) 5
 * +d) 1&minus;s
 * -e) s&minus;1

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 x component of the electric field at  (x,y) =( 5a, 4a) is &beta;kQ/a2, where &beta; equals
 * -a) 1.76 x 10-3 unit
 * -b) 2.13 x 10-3 unit
 * -c) 2.59 x 10-3 unit
 * +d) 3.13 x 10-3 unit
 * -e) 3.79 x 10-3 unit

12) 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) 8
 * -b) s&minus;3
 * -c) 3&minus;s
 * -d) s&minus;7
 * +e) 7&minus;s

KEY:PhysicsCalc2:T1:V2
PhysicsCalc2152657831440 1) A proton is accelerated (at rest) from a plate held at 333.6 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) 2.5 x 105 m/s.
 * -d) 3.8 x 105 m/s.
 * -e) 5.7 x 105 m/s.

2) 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) =( 5a, 4a) is &beta;kQ/a2, where &beta; equals
 * -a) 1.76 x 10-3 unit
 * -b) 2.13 x 10-3 unit
 * -c) 2.59 x 10-3 unit
 * +d) 3.13 x 10-3 unit
 * -e) 3.79 x 10-3 unit

3) A 1.3 Farad capacitor charged with 1.9 Coulombs. What is the energy stored in the capacitor if the plates are 0.3 mm apart?
 * -a) 0.91 J.
 * -b) 1.05 J.
 * -c) 1.21 J.
 * +d) 1.39 J.
 * -e) 1.6 J.

4) 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
 * +b) 1&minus;s
 * -c) 5&minus;s
 * -d) s&minus;1
 * -e) s&minus;4

5) 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, $$\left |\int_{top}\vec\mathfrak F\cdot\hat n dA\right|\,$$ over the top surface of the cylinder.
 * -a) 6.201E+02
 * -b) 7.513E+02
 * -c) 9.102E+02
 * +d) 1.103E+03
 * -e) 1.336E+03

6) How fast is a 2355 eV electron moving?
 * -a) 1.9 x 107 m/s.
 * +b) 2.9 x 107 m/s.
 * -c) 4.3 x 107 m/s.
 * -d) 6.5 x 107 m/s.
 * -e) 9.7 x 107 m/s.

7) A 0.5 Farad capacitor charged with 1.3 Coulombs. What is the force between the plates if they are 0.7 mm apart?
 * -a) 1826 N.
 * -b) 2099 N.
 * +c) 2414 N.
 * -d) 2776 N.
 * -e) 3193 N.

8) 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) 2.86 x 10-1
 * +b) 3.47 x 10-1
 * -c) 4.2 x 10-1
 * -d) 5.09 x 10-1
 * -e) 6.17 x 10-1

9) 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;7
 * -b) 8
 * -c) s&minus;3
 * +d) 7&minus;s
 * -e) 3&minus;s

10) Integrate the line integral of $$\vec F = 2xy\hat x + 9.7x\hat y $$  from the origin to the point at x = 2.8 and y = 3.2
 * -a) 5.26E+01
 * -b) 5.62E+01
 * +c) 6.02E+01
 * -d) 6.44E+01
 * -e) 6.89E+01

11) 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) 2
 * -b) 1/2
 * -c) 3
 * -d) 2/3
 * +e) 3/2

12) A cylinder of radius, r=3, 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, $$\vec\mathfrak F = (2.37+2.6z)\rho^2\hat\rho +8.84z^3\hat z $$ 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) 7.465E+02
 * -b) 9.044E+02
 * -c) 1.096E+03
 * -d) 1.327E+03
 * +e) 1.608E+03