The force between two point charges in a vacuum is F = Q1Q2/(4\pi\varepsilon0 r^2).

What is the value of ε₀?

8.85 \times 10^{-12}\ F\,m^{-1}.

Do like charges attract or repel?

Like charges repel; unlike charges attract.

What happens to the force if the separation is halved?

It increases by a factor of four.

Can air be treated as a vacuum in Coulomb's law?

Yes: the permittivity of air is almost the same as ε₀.

Where is the charge of a charged sphere considered to act?

At its centre, so r is measured between centres.

How do the forces on two charges compare?

Equal in magnitude and opposite in direction.

What is the value of 1/(4πε₀)?

About 8.99 \times 10^{9}\ N\,m^2\,C^{-2}.

Compare electrostatic and gravitational forces between a proton and an electron.

The electrostatic force is about 10³⁹ times larger.

Why is the force ratio between a proton and an electron independent of r?

Both forces follow an inverse square law, so r² cancels.

Why does gravity dominate for planets?

Planets are almost electrically neutral so electrostatic forces cancel, but gravitational forces always add.

Give a difference between electric and gravitational forces.

Electric forces can attract or repel; gravity only attracts.

Coulomb's lawAQA A-Level Physics: Flashcards

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State Coulomb's law.

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State Coulomb's law.: The force between two point charges in a vacuum is $F = Q_1Q_2/(4\pi\varepsilon_0 r^2)$ .
What is the value of ε₀?: $8.85 \times 10^{-12}\ \mathrm{F\,m^{-1}}$ .
Do like charges attract or repel?: Like charges repel; unlike charges attract.
What happens to the force if the separation is halved?: It increases by a factor of four.
What happens to the force if one charge is trebled?: It becomes three times larger.
Can air be treated as a vacuum in Coulomb's law?: Yes: the permittivity of air is almost the same as ε₀.
Where is the charge of a charged sphere considered to act?: At its centre, so r is measured between centres.
How do the forces on two charges compare?: Equal in magnitude and opposite in direction.
What is the value of 1/(4πε₀)?: About $8.99 \times 10^{9}\ \mathrm{N\,m^2\,C^{-2}}$ .
Compare electrostatic and gravitational forces between a proton and an electron.: The electrostatic force is about 10³⁹ times larger.
Why is the force ratio between a proton and an electron independent of r?: Both forces follow an inverse square law, so r² cancels.
Why does gravity dominate for planets?: Planets are almost electrically neutral so electrostatic forces cancel, but gravitational forces always add.
Give a difference between electric and gravitational forces.: Electric forces can attract or repel; gravity only attracts.

Exam questions on Coulomb's law

Two small metal spheres in air carry charges of +3.0 nC and −5.0 nC. Their centres are 4.0 cm apart.
Calculate the magnitude of the electrostatic force between the spheres. Use $\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F\,m^{-1}}$ .2 marks
In a hydrogen atom an electron orbits a proton. The mean separation of the particles is 5.3 × 10⁻¹¹ m. A student compares the electrostatic and gravitational forces between them.
Calculate the ratio of the electrostatic force to the gravitational force between the proton and the electron, and state why the ratio does not depend on their separation. Use $e = 1.60 \times 10^{-19}$ C, $m_e = 9.11 \times 10^{-31}$ kg, $m_p = 1.67 \times 10^{-27}$ kg, $G = 6.67 \times 10^{-11}\ \mathrm{N\,m^2\,kg^{-2}}$ and $\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F\,m^{-1}}$ .2 marks
A charged metal sphere of radius 2.0 cm carries a charge of +8.0 nC. A small ball carrying −2.0 nC is held in air with its centre 10.0 cm from the centre of the sphere.
Calculate the magnitude of the electrostatic force between the sphere and the ball. Use $\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{F\,m^{-1}}$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).