OpenStax University Physics/Archived sample/T1V1

PhysicsCalc2152657831440

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