Q: A proton is placed in a uniform electric field of $$500\ \mathrm{N/C}$$ pointing to the right. What is the magnitude and direction of the force on the proton?

$$8.01 \times 10$$^{-17}$$\ \mathrm{N} to $$the right

Q: A solid metal sphere of diameter $$11\ \mathrm{cm}$$ has a net charge of $$-7.20\ \mathrm{C}. $$What is the electric potential just outside its surface? (Assume $$V=0 at $$infinity and $$k_e = 8.988 \times 10^9$\ \mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^2)$$

$$-5.89 \times 10$$^{10}$$\ \mathrm{V}$$

Q: A large, neutral metal sheet of thickness $$3.2\ \mathrm{mm} is $$placed in an electric field of $$420\ \mathrm{kV/m}$$ perpendicular to the sheet. What is the induced surface charge density $$\sigma on $$each side of the sheet? (Use $$\$$epsilon_0$$ = 8.854 \times 10$$^{-12}$$\ \mathrm{C}^2/\mathrm{N} \cdot \mathrm{m}^2)$$

$$3.72 \times 10$$^{-6}$$\ \mathrm{C/m}^2$$

Question 1

Which of the following correctly expresses the electric field $$\vec{E}$$ due to a point charge $$q at a $$distance $$r in $$vacuum?

Accepted Answer

$$\vec{E} = k_e \dfrac{q}{r^2$} \hat{r}$$

Question 2

Given the SI base units, which of the following is equivalent to the unit of electric field strength (N/C)?

Accepted Answer

$$\mathrm{kg} \cdot \mathrm{m} \cdot \mathrm{s}^{-3} \cdot \mathrm{A}^{-1}$$

Question 3

A proton is placed in a uniform electric field of $$500\ \mathrm{N/C}$$ pointing to the right. What is the magnitude and direction of the force on the proton?

Accepted Answer

$$8.01 	imes 10$$^{-17}$$\ \mathrm{N} to $$the right

Question 4

Which equation correctly relates the change in electric potential energy $$\Delta U to $$the charge $$q$$ and change in electric potential $$\Delta V$$?

Accepted Answer

$$\Delta U = q \Delta V$$

Question 5

A solid metal sphere of diameter $$11\ \mathrm{cm}$$ has a net charge of $$-7.20\ \mathrm{C}. $$What is the electric potential just outside its surface? (Assume $$V=0 at $$infinity and $$k_e = 8.988 	imes 10^9$\ \mathrm{N} \cdot \mathrm{m}^2/\mathrm{C}^2)$$

Accepted Answer

$$-5.89 	imes 10$$^{10}$$\ \mathrm{V}$$

Question 6

If the electric potential $$V(x)$$ varies only with $$x as$$ $$V(x) = -2\pi k_e q |x|$$, what is the expression for the electric field $$E_x(x)$$?

Accepted Answer

$$E_x(x) = 2\pi k_e q \dfrac{x}{|x|}$$

Question 7

Which statement about conductors in electrostatic equilibrium is correct?

Accepted Answer

The electric field inside the conductor is zero and the potential is constant throughout the conductor.

Question 8

A large, neutral metal sheet of thickness $$3.2\ \mathrm{mm} is $$placed in an electric field of $$420\ \mathrm{kV/m}$$ perpendicular to the sheet. What is the induced surface charge density $$\sigma on $$each side of the sheet? (Use $$\$$epsilon_0$$ = 8.854 	imes 10$$^{-12}$$\ \mathrm{C}^2/\mathrm{N} \cdot \mathrm{m}^2)$$

Accepted Answer

$$3.72 	imes 10$$^{-6}$$\ \mathrm{C/m}^2$$

Question 9

Which of the following correctly expresses the relationship between electric field and electric potential in one dimension?

Accepted Answer

$$E_x = -\dfrac{dV}{dx}$$

Question 10

Two identical positive point charges are placed symmetrically on the $$y-$$axis at $$y = +a$$ and $$y = -a. $$What is the electric potential $$V at a $$point $$P on $$the $$x-$$axis at $$x = d$$?

Accepted Answer

$$V = 2k_e \dfrac{q}{\sqrt{a^2$ + d^2$}}$$

Question 11

Which of the following is true about equipotential surfaces and electric field lines?

Accepted Answer

Equipotential surfaces are always perpendicular to electric field lines.

Question 12

A charge $$q$$ moves a distance $$d$$ parallel to a uniform electric field $$E. $$What is the work done by the field?

Accepted Answer

$$W = qEd$$

Question 13

If the electric field in a region is constant, what can be said about the electric potential in that region?

Accepted Answer

The electric potential changes linearly with position.

Question 14

Which of the following is the correct expression for the potential energy $$U of a $$system of two point charges $$q_1$$ and $$q_2$$ separated by distance $$r_{12}$$?

Accepted Answer

$$U = k_e \dfrac{q_1$ q_2$}{r_{12}}$$

Question 15

A particle of mass $$m$$ and charge $$q is $$released from rest in a uniform electric field $$E. $$What is its speed after moving a distance $$d$$?

Accepted Answer

$$v = \sqrt{\dfrac{2qEd}{m}}$$

Question 16

Which of the following prefixes corresponds to $$10^{-6}$$?

Accepted Answer

$$\mu ($$micro)

Question 17

If $$V(x) is $$plotted as a straight line with negative slope, what does the corresponding $$E_x(x)$$ plot look like?

Accepted Answer

A horizontal line with constant positive value

Question 18

Which of the following is the correct vector form for the electric field from the gradient of potential?

Accepted Answer

$$\vec{E} = -\left( \dfrac{\partial V}{\partial x} \hat{i} + \dfrac{\partial V}{\partial y} \hat{j} + \dfrac{\partial V}{\partial z} \hat{k} \right)$$

Electric Energy and Potential: Field, Potential, and Applications

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