Practice Electric Potential in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The electric potential energy per unit charge at a point in an electric field. Measured in volts (V).

Electric potential is like altitude on a hill — charges 'roll downhill' from high potential to low potential, just as balls roll from high ground to low ground.

Showing a random 20 of 50 problems.

Example 1

easy
Find the energy of a +3 C+3 \text{ C} charge at a point where V=4 VV = 4 \text{ V}.

Example 2

medium
What is the electric potential 0.3 m0.3 \text{ m} from a point charge of 6×10−6 C6 \times 10^{-6} \text{ C}? Use k=9×109 N m2/C2k = 9 \times 10^9 \text{ N m}^2/\text{C}^2.

Example 3

hard
Two parallel plates separated by 2 cm2\ \text{cm} have a field of 4000 V/m4000\ \text{V/m}. What is the potential difference? An electron starts at rest at the negative plate; find its KE on reaching the positive plate.

Example 4

hard
A proton (q=+1.6×10−19 Cq = +1.6\times10^{-19}\ \text{C}, m=1.67×10−27 kgm = 1.67\times10^{-27}\ \text{kg}) is accelerated from rest through 1000 V1000\ \text{V}. Find its final speed.

Example 5

easy
A potential at r=5 mr = 5\ \text{m} from a charge is 40 V40\ \text{V}. What is it at r=10 mr = 10\ \text{m}?

Example 6

hard
A surface inside a hollow conductor (no charges inside) has potential V0V_0 at the wall. What is VV at the center of the cavity?

Example 7

hard
A uniform electric field of E=500 N/CE = 500 \text{ N/C} exists between two parallel plates separated by d=0.02 md = 0.02 \text{ m}. (a) What is the potential difference between the plates? (b) How much work is done moving a proton (q=1.6×10−19 Cq = 1.6 \times 10^{-19} \text{ C}) from the negative to the positive plate?

Example 8

easy
What are the units of electric potential?

Example 9

easy
Charges 'roll' from high to low potential. Which way does a positive charge move if released?

Example 10

easy
Find the potential at r=1r=1 m from a +1+1 C charge. Use k=9×109k=9\times10^9.

Example 11

easy
Potential at r=2r=2 m from a charge is 9 V9 \text{ V}. What is it at r=4r=4 m?

Example 12

medium
A +2 μC+2\ \mu\text{C} charge moves from 50 V50\ \text{V} to 10 V10\ \text{V}. How much kinetic energy can it gain (assuming no losses)?

Example 13

medium
At what distance from a +5+5 C charge is the potential 1×1091\times10^9 V? Use k=9×109k=9\times10^9.

Example 14

medium
Two parallel plates are 0.05 m0.05\ \text{m} apart with ΔV=250 V\Delta V = 250\ \text{V}. Find the uniform field between them.

Example 15

medium
A point is 0.10 m0.10\ \text{m} from +5 μC+5\ \mu\text{C} and 0.20 m0.20\ \text{m} from −5 μC-5\ \mu\text{C}. Find the total potential. Use k=9×109k = 9\times10^9.

Example 16

medium
A charge moves and gains 5050 J crossing a 1010 V difference. Find the charge.

Example 17

easy
True or false: electric potential is a vector quantity.

Example 18

medium
An electron is accelerated through 250 V250\ \text{V}. Find its kinetic energy gain.

Example 19

medium
An electron (q=−1.6×10−19 Cq = -1.6 \times 10^{-19} \text{ C}) is accelerated through a potential difference of 1000 V1000 \text{ V}. What kinetic energy does it gain?

Example 20

medium
A charge gains 3030 J moving through a region. If the charge is 66 C, find the potential difference it crossed.
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