Question 1

A positive charge is released from rest in an electric field. Which direction does it move, and why?

Accepted Answer

Toward lower electric potential, because it loses potential energy and gains kinetic energy.

Question 2

The electric potential $$V at a $$distance $$r$$ from a point charge $$q is $$given by which equation?

Accepted Answer

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

Question 3

Three electrons are spaced 1.0 mm apart along a vertical line. The outer two electrons are fixed. If the center electron is displaced horizontally by a small distance, what will happen?

Accepted Answer

It will accelerate away from the line, indicating unstable equilibrium.

Question 4

A water molecule (electric dipole) is aligned in an electric field $$E. $$How much energy is needed to rotate the molecule by $$90^\circ$$?

Accepted Answer

$$U = pE$$

Question 5

A proton with initial speed $$v_0 = 2.0$$ 	imes $$10^5 m/s $$enters a region with a potential difference of $$\Delta V = 100 V. $$What is its final speed?

Accepted Answer

$$v_f = \sqrt{v_0$^2 + \frac{2e\Delta V}{m_p}}$$

Question 6

The electric field inside a parallel-plate capacitor with voltage $$\Delta V$$ and plate separation $$d is$$:

Accepted Answer

$$E = \frac{\Delta V}{d}$$

Question 7

If two protons are launched from the same point with the same speed but follow different trajectories, how are their speeds at different points related?

Accepted Answer

The proton at the point of lower potential will have higher speed.

Question 8

What is the ratio $$V_B/V_A of $$the electric potentials at two points, B and A, if B is three times closer to a point charge than A?

Accepted Answer

9

Question 9

Outside a uniformly charged sphere of radius $$R$$ and charge $$Q$$, the electric potential at distance $$r \geq R is$$:

Accepted Answer

$$V = \frac{Q}{4\pi\$$epsilon_0$$ r}$$

Question 10

The electric potential at a point due to multiple point charges is:

Accepted Answer

$$V = \sum_i \frac{q_i}{4\pi\$$epsilon_0$$ r_i}$$

Question 11

The potential difference between two points in space, given the electric field $$E$$ along a path $$ds$$, is:

Accepted Answer

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

Question 12

The electric field in the $$s-$$direction can be found from the electric potential $$V as$$:

Accepted Answer

$$E_s = -\frac{dV}{ds}$$

Question 13

Which statement about a conductor in electrostatic equilibrium is correct?

Accepted Answer

The electric field inside the conductor is zero.

Question 14

Metal wires are attached to the terminals of a 3 V battery. What is the potential difference between two points on the same wire?

Accepted Answer

0 V

Question 15

Two metal spheres are connected by a metal wire. Which quantities do they have in common?

Accepted Answer

Same potential

Question 16

A proton is released from rest at the surface of a sphere charged to $$+1000 V. $$What is the charge $$Q of $$the sphere of radius $$r$$?

Accepted Answer

$$Q = 4\pi\$$epsilon_0$$ r V$$

Question 17

The electric field units V/m are equivalent to which other units?

Accepted Answer

N/C

Question 18

At the midpoint between two equal but opposite charges, what is the electric potential?

Accepted Answer

Zero

Question 19

If the electric potential changes by 20 V over a distance of 2 m, what is the magnitude and direction of the electric field?

Accepted Answer

$$E = 10 V/m$$, pointing toward lower potential

Electric Potential and Its Relationship to Electric Field

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