Question 1

Which of the following best describes the relationship between electric field $$\vec{E}$$ and electric potential $$V$$?

Accepted Answer

$$\vec{E} is $$the negative gradient of $$V$$: $$\vec{E} = -
abla V$$

Question 2

A parallel-plate capacitor has a uniform electric field of $$1500\ \mathrm{V/m}$$ and a plate separation of $$1\ \mathrm{mm}. $$What is the potential difference between the plates?

Accepted Answer

$$1.5\ \mathrm{V}$$

Question 3

The potential difference $$\Delta V$$ between two points in an electric field is given by which integral?

Accepted Answer

$$\Delta V = -\int_{i}^{f} \vec{E} \cdot d\vec{s}$$

Question 4

What is the electric potential $$V at a $$distance $$r$$ from a point charge $$q$$?

Accepted Answer

$$V = \dfrac{q}{4\pi\$$epsilon_0$$ r}$$

Question 5

If the electric field in a region is given by $$E_x = 1000x\ \mathrm{V/m}$$, what is the potential difference $$\Delta V$$ between $$x=0$$ and $$x=2\ \mathrm{m}$$?

Accepted Answer

$$-2000\ \mathrm{V}$$

Question 6

A charge $$q$$ moves a small distance $$\Delta s in a $$uniform electric field $$E_s. $$What is the change in electric potential $$\Delta V$$?

Accepted Answer

$$\Delta V = -E_s \Delta s$$

Question 7

Which of the following is true about the direction of the electric field relative to equipotential surfaces?

Accepted Answer

The electric field is always perpendicular to equipotential surfaces.

Question 8

Given the potential $$V(x) = -500x^2$ (in volts, with x$ in meters), what is the electric field E_x$ as a function of x$?

Accepted Answer

$$E_x = -1000x$$

Question 9

A region of space has a constant electric field $$\vec{E}. $$What is the shape of the electric potential $$V as a $$function of position along the field direction?

Accepted Answer

Linear

Question 10

In a parallel-plate capacitor, the electric field between the plates is $$E = 2000\ \mathrm{V/m}$$ and the plates are $$0.5\ \mathrm{cm}$$ apart. What is the potential difference between the plates?

Accepted Answer

$$1\ \mathrm{V}$$

Question 11

Which of the following steps is NOT part of the recommended procedure for finding the potential from the electric field?

Accepted Answer

Calculate the curl of the electric field.

Question 12

If the electric potential $$V is $$constant in a region of space, what can you conclude about the electric field $$\vec{E} in $$that region?

Accepted Answer

$$\vec{E} is $$zero everywhere in that region.

Question 13

A positive charge is released from rest in a region of decreasing electric potential. What happens to its kinetic energy?

Accepted Answer

It increases.

Question 14

Which of the following correctly expresses the work done by the electric field when a charge $$q$$ moves from point $$i to $$point $$f$$?

Accepted Answer

$$W = -q(V_f - V_i)$$

Question 15

The electric field at a distance $$r$$ from a point charge $$q is $$given by:

Accepted Answer

$$E = \dfrac{q}{4\pi\$$epsilon_0$$ r^2$}$$

Question 16

If the slope of the potential $$V(x)$$ versus $$x is$$ $$-500\ \mathrm{V/m}$$, what is the value of the electric field $$E_x$$?

Accepted Answer

$$E_x = 500\ \mathrm{V/m}$$

Question 17

A region of space has the potential $$V(x) = 10 - 2x (in $$volts, with $$x in $$meters). What is the electric field $$E_x$$?

Accepted Answer

$$E_x = 2\ \mathrm{V/m}$$

Question 18

Which of the following statements about the relationship between force, field, potential energy, and potential is correct?

Accepted Answer

Force and potential energy are local concepts, while electric field and potential are defined everywhere in space.

Electric Potential and Electric Field: Chapter 26 Study Notes

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