Q: An electron moves from the ground to a cloud with a potential difference of $$1.2 \times 10^9$\ \text{V}. $$What is the change in energy (in electron-volts) of the electron?

$$1.2 \times 10^9$\ \text{eV}$$

Q: A conducting sphere of radius $$0.15\ \text{m}$$ has a potential of $$200\ \text{V} ($$with $$V = 0 at $$infinity). What is the charge density on its surface?

$$1.2 \times 10$$^{-8}$$\ \text{C}/\text{m}^2$$

Q: What is the potential energy of two electrons separated by $$2.00\ \text{nm}$$?

$$1.15 \times 10$$^{-19}$$\ \text{J}$$

Q: Two electrons are fixed $$2.0\ \text{cm}$$ apart. A third electron is shot from infinity and stops midway between them. What is its initial speed?

$$3.18 \times 10^2$\ \text{m}/\text{s}$$

Question 1

A charge $$q$$ moves from point $$r_1 to$$ $$r_2 in a $$constant electric field $$\mathbf{E}. $$Which expression correctly gives the work done by the electric field on the charge?

Accepted Answer

$$W = q \int_{r_1$}^{r_2$} \mathbf{E} \cdot d\mathbf{s}$$

Question 2

Which statement about electric potential is correct?

Accepted Answer

Electric potential is a scalar quantity defined as the potential energy per unit charge.

Question 3

An electron moves from the ground to a cloud with a potential difference of $$1.2 	imes 10^9$\ 	ext{V}. $$What is the change in energy (in electron-volts) of the electron?

Accepted Answer

$$1.2 	imes 10^9$\ 	ext{eV}$$

Question 4

A nonconducting sheet has a surface charge density $$\sigma = 0.10\ \mu	ext{C}/	ext{m}^2. $$What is the distance between equipotential surfaces whose potentials differ by $$50\ 	ext{V}$$?

Accepted Answer

$$8.8\ 	ext{mm}$$

Question 5

Two parallel conducting plates are $$12\ 	ext{cm}$$ apart. An electron between the plates experiences a force of $$3.9 	imes 10$$^{-15}$$\ 	ext{N}. $$What is the potential difference between the plates?

Accepted Answer

$$2.9 	imes 10^3$\ 	ext{V}$$

Question 6

The electric field inside a nonconducting sphere of radius $$R$$ with total charge $$q is$$ $$E(r) = \frac{q r}{4 \pi \$$epsilon_0$$ R^3$}. If$$ $$V = 0 at $$the center, what is the electric potential at distance $$r$$ inside the sphere?

Accepted Answer

$$V(r) = -\frac{q r^2$}{8 \pi \$$epsilon_0$$ R^3$}$$

Question 7

A charge $$q is $$distributed uniformly throughout a sphere of radius $$R. $$With $$V = 0 at $$infinity, what is the potential at a distance $$r \u003c R$$ from the center?

Accepted Answer

$$V(r) = \frac{q (3R^2$ - r^2$)}{8 \pi \$$epsilon_0$$ R^3$}$$

Question 8

A conducting sphere of radius $$0.15\ 	ext{m}$$ has a potential of $$200\ 	ext{V} ($$with $$V = 0 at $$infinity). What is the charge density on its surface?

Accepted Answer

$$1.2 	imes 10$$^{-8}$$\ 	ext{C}/	ext{m}^2$$

Question 9

The electric potential at points in an $$xy$$ plane is $$V = (2.0\ 	ext{V}/	ext{m}^2)x^2$ - (3.0\ 	ext{V}/	ext{m}^2)y^2$. What is the magnitude of the electric field at (3.0$$\ 	ext{m}, 2.0\ 	ext{m})$$?

Accepted Answer

$$17\ 	ext{V}/	ext{m}$$

Question 10

What is the potential energy of two electrons separated by $$2.00\ 	ext{nm}$$?

Accepted Answer

$$1.15 	imes 10$$^{-19}$$\ 	ext{J}$$

Question 11

A system consists of four charges arranged at the corners of a square, each side of length $$a$$, with charges $$+q$$, $$-q$$, $$+q$$, $$-q. $$What is the total work required to assemble this system from infinity?

Accepted Answer

$$W = \frac{q^2$}{4 \pi \$$epsilon_0$$ a}(-4 + 2\sqrt{2})$$

Question 12

In a rectangle with sides $$5.0\ 	ext{cm}$$ and $$15\ 	ext{cm}$$, charges $$q_1 = -5.0$$\ \mu	ext{C}$$ and q_2$ = +2.0\ \mu	ext{C}$$ are placed at adjacent corners. What is the electric potential at the corner $$A$$ that is $$15\ 	ext{cm}$$ from $$q_1$$ and $$5.0\ 	ext{cm}$$ from $$q_2$$?

Accepted Answer

$$6.0 	imes 10^4$\ 	ext{V}$$

Question 13

How much work is required to move a charge $$q_3 = +3.0$$\ \mu	ext{C}$$ from corner B$ to corner A$ in the rectangle described above?

Accepted Answer

$$2.5\ 	ext{J}$$

Question 14

Two tiny metal spheres $$A$$ and $$B of $$masses $$m_A = 5.00\ 	ext{g}$$ and $$m_B = 10.0\ 	ext{g}$$, each with charge $$q = 5.00\ \mu	ext{C}$$, are connected by a string of length $$1.00\ 	ext{m}. If $$the string is cut, what is the initial acceleration of sphere $$A$$?

Accepted Answer

$$45.0\ 	ext{m}/	ext{s}^2$$

Question 15

After the string is cut in the previous question, what is the speed of sphere $$A$$ when the spheres are very far apart?

Accepted Answer

$$7.75\ 	ext{m}/	ext{s}$$

Question 16

Two electrons are fixed $$2.0\ 	ext{cm}$$ apart. A third electron is shot from infinity and stops midway between them. What is its initial speed?

Accepted Answer

$$3.18 	imes 10^2$\ 	ext{m}/	ext{s}$$

Question 17

Which of the following statements about equipotential surfaces is correct?

Accepted Answer

Equipotential surfaces are always perpendicular to electric field lines.

Question 18

Given the electric potential $$V(r)$$, how do you find the electric field $$\mathbf{E}$$?

Accepted Answer

$$\mathbf{E} = -
abla V$$

Chapter 4: The Electric Potential – Study Notes

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