Coulomb's Law Examples: 45 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Coulomb's Law.

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

Concept Recap

Coulomb's law gives the electric force between two point charges. The force gets larger when the charges are larger and gets smaller with the square.

Like gravity between masses, but for charges. Double the distance and the force drops to one quarter. Double either charge and the force doubles.

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: Coulomb's Law 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 coulomb's law 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

Two charges

q_1 = 3 \times 10^{-6} \text{ C}

and

q_2 = 5 \times 10^{-6} \text{ C}

are separated by

0.2 \text{ m}

. What is the electrostatic force between them? Use

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

Electrostatic force on q₁ (q₁=3μC, q₂=5μC, r=0.2 m)

Answer

F = 3.375 N

First step

Apply Coulomb's law:

F = k \frac{∣ q_{1} q_{2} ∣}{r^{2}}

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Example 2

hard

Two identical charges experience a force of

0.1 \text{ N}

when separated by

0.3 \text{ m}

. What is the magnitude of each charge?

Example 3

medium

Two identical charges

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

repel with

9\text{ N}

. Find the separation. Use

k = 9\times 10^9

Example 4

medium

Two protons are

10^{-10}\text{ m}

apart. Find the magnitude of the Coulomb force. Use

k = 9\times 10^9

and

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

Example 5

hard

Two

+2\,\mu\text{C}

charges sit at

(0, 0.3\text{ m})

and

(0, -0.3\text{ m})

. Find the magnitude of the force on a

+1\,\mu\text{C}

charge placed at

(0.4\text{ m}, 0)

. Use

k = 9\times 10^9

Practice Problems

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

Example 1

medium

If the distance between two charges is tripled, by what factor does the electrostatic force change?

Example 2

hard

Two charges

q_1 = +4 \times 10^{-6} \text{ C}

and

q_2 = -2 \times 10^{-6} \text{ C}

are separated by

0.1 \text{ m}

. (a) Calculate the force between them. (b) Is the force attractive or repulsive? Use

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

Force on +4μC charge; q₂

Example 3

easy

Two charges

q_1=2 \text{ C}

q_2=3 \text{ C}

are

r=3 \text{ m}

apart. Find the force. Use

k=9\times10^9

Example 4

easy

Like charges: do they attract or repel?

Example 5

easy

If the distance between two charges doubles, the force changes by what factor?

Example 6

easy

Two

1 \text{ C}

charges are

1 \text{ m}

apart. Find the force. Use

k=9\times10^9

Example 7

easy

If you double one of the two charges, the force changes by what factor?

Example 8

easy

Unlike charges (one

+

, one

-

): attract or repel?

Example 9

easy

What is the value and units of Coulomb's constant

k

Example 10

easy

Charges

q_1=5 \text{ C}

q_2=2 \text{ C}

, separation

r=10 \text{ m}

. Find the force. Use

k=9\times10^9

Example 11

medium

Two charges repel with

8 \text{ N}

2 \text{ m}

. What is the force at

1 \text{ m}

Find the new repulsive force when r goes from 2 m to 1 m (original F

Example 12

medium

Charges

q_1=4\times10^{-6}

C and

q_2=6\times10^{-6}

C are

r=2 \text{ m}

apart. Find the force. Use

k=9\times10^9

Example 13

medium

Two equal charges

q

are

3 \text{ m}

apart and repel with

10 \text{ N}

. Find

q

. Use

k=9\times10^9

Example 14

medium

Three charges in a line:

+2

C at

x=0

+2

C at

x=2

m. Find the net force on a

+1

C charge at

x=1

m. Use

k=9\times10^9

+1 C at x=1 m between +2 C at x=0 and +2 C at x=2 m; net force

Example 15

medium

A force of

36 \text{ N}

acts between two charges. If one charge triples and the distance doubles, find the new force.

Example 16

medium

Two charges feel

20 \text{ N}

. If both charges double, find the new force.

Example 17

medium

At what separation do charges

+3

C and

+3

C repel with

9\times10^9 \text{ N}

? Use

k=9\times10^9

Example 18

medium

Compare the Coulomb force between two protons (

q=1.6\times10^{-19}

C) at

r=1

m: find its magnitude. Use

k=9\times10^9

Example 19

challenge

Charges

+q

(0,0)

+q

(d,0)

+q

(0,d)

. Find the magnitude of the net force on the charge at the origin in terms of

k,q,d

Example 20

challenge

A charge

+q

x=0

and

+4q

x=L

. Where on the segment is the net force on a test charge zero?

Example 21

challenge

Two pith balls each of mass

m = 0.01

kg hang from threads and carry equal charge

q

. They hang

30°

from vertical,

0.1

m apart. Estimate

q

. Use

k = 9 \times 10^9

N·m²/C²,

g = 10

m/s².

Example 22

medium

A charge

+q

x=0

and

+4q

x=L

. Find where on the segment the net force on a test charge is zero.

Example 23

easy

Two charges

q_1 = 2\,\mu\text{C}

and

q_2 = 3\,\mu\text{C}

are separated by

0.3\text{ m}

. Find the magnitude of the force. Use

k = 9\times 10^9

N·m²/C².

Force on q₁

Example 24

easy

Two

+1\,\mu\text{C}

charges are

0.1\text{ m}

apart. Find the force. Use

k = 9\times 10^9

N·m²/C².

Example 25

easy

+2\,\mu\text{C}

and a

-2\,\mu\text{C}

charge are

0.2\text{ m}

apart. Find the force. Use

k = 9\times 10^9

+2μC and −2μC at r=0.2 m; attractive force

Example 26

easy

If you halve the distance between two charges, the force becomes ___ times larger.

Example 27

medium

Two charges experience

12\text{ N}

0.5\text{ m}

. Find the force at

0.25\text{ m}

Original F = 12 N at r = 0.5 m; find new force at r

Example 28

medium

Two charges with

F = 10\text{ N}

. If one charge is quintupled and distance doubles, find the new force.

Example 29

medium

Charges

+5\,\mu\text{C}

and

-2\,\mu\text{C}

are

0.4\text{ m}

apart. Find the force magnitude. Use

k = 9\times 10^9

+5μC and −2μC at r=0.4 m; F ≈ 0.563 N attractive

Example 30

medium

Three charges in a line:

+1\,\mu\text{C}

x=0

-1\,\mu\text{C}

x=2

m. Find the force on a

+1\,\mu\text{C}

test charge at

x=1

m. Use

k = 9\times 10^9

Test charge at x=1 m: repelled left (+1μC at 0) and attracted right (−1μC at 2 m); net

Example 31

medium

+4\,\mu\text{C}

charge is at the origin and a

+9\,\mu\text{C}

charge is at

x = 5\text{ m}

. Where on the segment is the net force on a positive test charge zero?

Example 32

medium

Two identical small spheres each carry charge

q

and are

0.1\text{ m}

apart with a force of

0.36\text{ N}

. Find

q

. Use

k = 9\times 10^9

Example 33

medium

Two charges feel a force of

4\text{ N}

. If both charges triple and the distance halves, find the new force.

Original F = 4 N; both charges ×3, distance ×½ → new F = ?

Example 34

hard

Four equal charges

+q

sit at the corners of a square of side

a

. Find the net force on one corner charge in terms of

kq^2/a^2

Net force on one corner of a square of four +q charges

Example 35

hard

Two identical pith balls (each

5\text{ g}

) hang from

0.5\text{ m}

silk threads and repel until they are

0.04\text{ m}

apart, hanging at

\theta

from vertical. Estimate the charge on each. Use

g = 10\text{ m/s}^2

k = 9\times 10^9

FBD of 5 g pith ball; balls 0.04 m apart on 0.5 m threads — find charge q

Example 36

hard

Three charges in a line:

+q

x=0

-2q

x=L

, and a test

+q

x=2L

. Find the net force on the test charge in terms of

kq^2/L^2

+q at 0, −2q at L, test +q at 2L; net force

Example 37

hard

Two charges

+3\,\mu\text{C}

and

+12\,\mu\text{C}

are

0.6\text{ m}

apart. Where on the segment between them is the electric field zero?

+3μC at 0, +12μC at 0.6 m — electric field zero at x

Example 38

hard

Two metal spheres of charges

+8\,\mu\text{C}

and

-2\,\mu\text{C}

are touched together briefly and separated to

0.3\text{ m}

. Find the new force between them. Use

k = 9\times 10^9

Example 39

challenge

A charge

+Q

sits at the origin and

+9Q

x = L

. A third charge

q

is placed somewhere between so it experiences zero net force. Find

x

Example 40

challenge

Three equal charges

+q

sit at the corners of an equilateral triangle of side

a

. Find the magnitude of the net force on one charge in terms of

kq^2/a^2

Net force on one charge of an equilateral triangle of three equal +q charges

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Related Concepts

Electric Charge Electric Field Electric Potential

Background Knowledge

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

electric chargeelectric field