Electric Potential Examples in Physics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Electric Potential.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Physics.

Concept 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.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Electric Potential starts by naming the source, the object affected, and how the field or potential changes through space.

Common stuck point: Students often know a formula related to electric potential but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

Sense of Study hint: Ask: Am I using a field or potential to explain how one object influences another across space?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Coulomb's Law Mistakes

Worked Examples

Example 1

medium

What is the electric potential

0.3 \text{ m}

from a point charge of

6 \times 10^{-6} \text{ C}

? Use

k = 9 \times 10^9 \text{ N m}^2/\text{C}^2

Answer

V = 1.8 \times 10^5 \text{ V}

First step

Use the electric potential formula for a point charge:

V = k\dfrac{q}{r}

, where

k = 9 \times 10^9\,\text{N m}^2/\text{C}^2

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Example 2

hard

How much work is needed to move a

3 \times 10^{-6} \text{ C}

charge from a point at

200 \text{ V}

to a point at

500 \text{ V}

Example 3

medium

An electron is accelerated through

250\ \text{V}

. Find its kinetic energy gain.

Example 4

medium

+2\ \mu\text{C}

charge moves from

50\ \text{V}

10\ \text{V}

. How much kinetic energy can it gain (assuming no losses)?

Example 5

hard

Find the potential energy of the pair:

+2\ \mu\text{C}

and

+3\ \mu\text{C}

separated by

0.10\ \text{m}

. Use

k = 9\times10^9

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

An electron (

q = -1.6 \times 10^{-19} \text{ C}

) is accelerated through a potential difference of

1000 \text{ V}

. What kinetic energy does it gain?

Example 2

hard

A uniform electric field of

E = 500 \text{ N/C}

exists between two parallel plates separated by

d = 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 \times 10^{-19} \text{ C}

) from the negative to the positive plate?

Example 3

easy

Find the potential at

r=3 \text{ m}

from a

+6 \text{ C}

charge. Use

k=9\times10^9

Example 4

easy

What are the units of electric potential?

Example 5

easy

Is electric potential a scalar or a vector?

Example 6

easy

+2 \text{ C}

charge has potential energy

10 \text{ J}

at a point. Find the potential.

Example 7

easy

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

Example 8

easy

Potential at

r=2

m from a charge is

9 \text{ V}

. What is it at

r=4

Example 9

easy

Find the energy of a

+3 \text{ C}

charge at a point where

V = 4 \text{ V}

Example 10

easy

Find the potential at

r=1

m from a

+1

C charge. Use

k=9\times10^9

Example 11

medium

Two charges

+2

C and

-2

C are each

2

m from a point. Find the total potential there. Use

k=9\times10^9

Example 12

medium

Potential from a charge is

V=kQ/r

. If

Q

doubles and

r

triples, by what factor does

V

change?

Example 13

medium

How much energy to bring a

+2

C charge from infinity to

r=3

m from a

+3

C charge? Use

k=9\times10^9

Example 14

medium

Two

+4

C charges are

r=2

m from a point on their perpendicular bisector... simpler: each is

2

m away. Find total potential. Use

k=9\times10^9

Example 15

medium

At what distance from a

+5

C charge is the potential

1\times10^9

V? Use

k=9\times10^9

Example 16

medium

A charge gains

30

J moving through a region. If the charge is

6

C, find the potential difference it crossed.

Example 17

medium

-3

C charge sits at

r=3

m from a

+6

C charge. Find the pair's potential energy. Use

k=9\times10^9

Example 18

challenge

On the line between

+q

x=0

and

-q

x=d

, where is the potential zero (besides infinity)? Express in terms of

d

Example 19

challenge

A charge

+q

is released from rest at

r_1=1

m from a fixed

+q

and flies to

r_2=2

m. Using energy conservation, find its kinetic energy gained in terms of

k,q

Example 20

challenge

Two parallel plates are

0.02

m apart with a uniform field

E=5000

N/C between them. Find the potential difference across the plates.

Example 21

medium

A charge moves and gains

50

J crossing a

10

V difference. Find the charge.

Example 22

medium

A point is

r=6

m from

+2

C and

r=3

m from

-1

C. Find the total potential. Use

k=9\times10^9

Example 23

easy

+4\ \text{C}

charge has potential energy

24\ \text{J}

at a point. Find the potential.

Example 24

easy

Find

V

r = 2\ \text{m}

from a

+4\ \text{C}

point charge. Use

k = 9\times10^9

Example 25

easy

What is the SI unit of electric potential, expressed in base SI units (besides volts)?

Example 26

easy

A potential at

r = 5\ \text{m}

from a charge is

40\ \text{V}

. What is it at

r = 10\ \text{m}

Example 27

easy

A point is

r = 1\ \text{m}

from

+1\ \text{C}

and

r = 1\ \text{m}

from

-1\ \text{C}

. Find the total potential. Use

k = 9\times10^9

Example 28

medium

Two parallel plates are

0.05\ \text{m}

apart with

\Delta V = 250\ \text{V}

. Find the uniform field between them.

Example 29

medium

Two charges

+3\ \mu\text{C}

and

+5\ \mu\text{C}

are each

0.10\ \text{m}

from a point. Find the total potential. Use

k = 9\times10^9

Example 30

medium

A capacitor stores

0.05\ \text{J}

when charged to

100\ \text{V}

. How much charge does it hold? (Use

U = \tfrac{1}{2}QV

Example 31

medium

At what distance from a

+3\ \mu\text{C}

charge is

V = 1000\ \text{V}

? Use

k = 9\times10^9

Example 32

medium

How much work must an external agent do to move a

+2\ \mu\text{C}

charge from

10\ \text{V}

60\ \text{V}

Example 33

medium

Charges

+q

(0,0)

and

-q

(d,0)

. Find the potential at

(d/2, 0)

Example 34

medium

A point is

0.10\ \text{m}

from

+5\ \mu\text{C}

and

0.20\ \text{m}

from

-5\ \mu\text{C}

. Find the total potential. Use

k = 9\times10^9

Example 35

hard

A proton (

q = +1.6\times10^{-19}\ \text{C}

m = 1.67\times10^{-27}\ \text{kg}

) is accelerated from rest through

1000\ \text{V}

. Find its final speed.

Example 36

hard

Two parallel plates separated by

2\ \text{cm}

have a field of

4000\ \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 37

hard

A point charge

+Q

creates

V = 200\ \text{V}

r = 3\ \text{m}

. Find

V

r = 0.5\ \text{m}

Example 38

hard

An electron starts from rest and is accelerated through a potential difference

V

to a final speed of

1.0\times10^7\ \text{m/s}

. Find

V

. (

m_e = 9.11\times10^{-31}\ \text{kg}

e = 1.6\times10^{-19}\ \text{C}

Example 39

hard

A point charge has

V = 50\ \text{V}

r_1 = 4\ \text{m}

. How much work must be done to bring a

+1\ \mu\text{C}

test charge from infinity to

r = 2\ \text{m}

from the source?

Example 40

challenge

Three

+q

charges sit at the vertices of an equilateral triangle of side

a

. Find the total potential at the centroid.

Example 41

challenge

Two charges

-2\ \mu\text{C}

x=0

and

+8\ \mu\text{C}

x=1\ \text{m}

. Locate all points on the x-axis (excluding infinity) where the potential is zero.

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Related Concepts

Electric Field Coulomb's Law Potential Difference

Background Knowledge

These ideas may be useful before you work through the harder examples.

electric fieldcoulombs law