The distance between two charges is doubled. What happens to the force between them?

It falls to a quarter. The force is proportional to 1 ÷ r².

Both of two charges are doubled, and the distance stays the same. What happens to the force between them?

It becomes four times bigger. The force is proportional to the product of the charges.

How does the field strength at a distance 2r from a point charge compare with the field strength at r?

It is a quarter as big. E is proportional to 1 ÷ r².

For points outside a charged conducting sphere, where does its charge seem to be?

at its centre. The same idea as treating a planet's mass as being at its centre.

Coulomb's law and point charges · Cambridge A Level Physics

In plain words

Two charges push or pull on each other with a force that follows the same pattern as gravity: it depends on both charges, and falls off with the square of the distance. The big differences are that it can repel as well as attract, and that it is enormously stronger.

5 things to know

Coulomb's law: F = Q₁Q₂ ÷ 4πε₀r², where ε₀ = 8.85 × 10⁻¹² F/m. The constant 1 ÷ 4πε₀ is 8.99 × 10⁹ N m² C⁻². Like charges repel and unlike charges attract.
For any point outside a charged conducting sphere, the charge behaves as if it were all at the centre.
The field strength at a distance r from a point charge Q is E = Q ÷ 4πε₀r².
Both are inverse square laws: at twice the distance, the force and the field strength are a quarter as big.
Field strength is a vector. To find the field due to several charges, add their fields with direction taken into account.

Worked example

Find the force between charges of +2.0 µC and +3.0 µC that are 0.10 m apart.

F = Q₁Q₂ ÷ 4πε₀r² = 8.99 × 10⁹ × 2.0 × 10⁻⁶ × 3.0 × 10⁻⁶ ÷ 0.10².
= 0.0539 ÷ 0.010.
= 5.4 N, and it is a repulsion, because both charges are positive.

Tips and tricks

Change µC and nC to coulombs and centimetres to metres, and remember to square r.
Work out the size of the force from the sizes of the charges, then decide the direction from their signs.

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Coulomb's law and point charges: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

The distance between two charges is doubled. What happens to the force between them?
- It halves.
- It falls to a quarter. (the answer)
- It doubles.
- It stays the same.
The force is proportional to 1 ÷ r².
What do two negative charges do to each other?
- repel (the answer)
- attract
- nothing
- attract, then repel
Like charges repel.
Both of two charges are doubled, and the distance stays the same. What happens to the force between them?
- It doubles.
- It becomes four times bigger. (the answer)
- It stays the same.
- It halves.
The force is proportional to the product of the charges.
How does the field strength at a distance 2r from a point charge compare with the field strength at r?
- It is a quarter as big. (the answer)
- It is half as big.
- It is the same.
- It is twice as big.
E is proportional to 1 ÷ r².
For points outside a charged conducting sphere, where does its charge seem to be?
- at its centre (the answer)
- spread over its surface
- at the nearest point of its surface
- at infinity
The same idea as treating a planet's mass as being at its centre.

5 questions

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Worksheet

4 questions, 9 marks. Write your answers on paper, then check them.

Coulomb's law and point charges

Cambridge International AS & A Level Physics 9702 · 9 marks · papermunch.org

Name ______________________________ Date ______________

Find the electric field strength 0.30 m from a point charge of +5.0 nC.[3]
Show answerHide answer
500 N/C. 8.99 × 10⁹ × 5.0 × 10⁻⁹ ÷ 0.30².
I got this one
The distance between two charges is tripled. State what happens to the force between them.[2]
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It falls to one ninth.
I got this one
Two equal positive charges are 0.20 m apart. State the field strength at the point midway between them, and explain your answer.[2]
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Zero. The fields due to the two charges are equal in size and opposite in direction there, so they cancel.
I got this one
State one similarity and one difference between electric fields and gravitational fields.[2]
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Similarity: both follow an inverse square law for a point source (or both are force fields that act at a distance). Difference: gravitational forces are always attractive, but electric forces can attract or repel.
I got this one

Answers: Coulomb's law and point charges

1. 500 N/C. 8.99 × 10⁹ × 5.0 × 10⁻⁹ ÷ 0.30².
2. It falls to one ninth.
3. Zero. The fields due to the two charges are equal in size and opposite in direction there, so they cancel.
4. Similarity: both follow an inverse square law for a point source (or both are force fields that act at a distance). Difference: gravitational forces are always attractive, but electric forces can attract or repel.