# Gravitational, electric and magnetic fields: Unit 3.4(a)

> state Newton law of gravitation and Coulomb law and compare their forms

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Specification statement (Unit 3.4(a)): state Newton law of gravitation and Coulomb law and compare their forms

## Explanation

1. **Newton's law of gravitation:** F = Gm₁m₂/r². **Coulomb's law:** F = Q₁Q₂/(4πε₀r²).
2. Both are **inverse-square** laws for point masses or charges (or spheres, measured from their centres): doubling r quarters the force.
3. Differences: gravity is always attractive and acts on mass; the electric force can attract or repel and acts on charge. The electric force between two protons is about 10³⁶ times the gravitational force.

## Worked example

Compare the electric and gravitational forces between two protons (Q = 1.60 × 10⁻¹⁹ C, m = 1.67 × 10⁻²⁷ kg, 1/4πε₀ = 8.99 × 10⁹ N m² C⁻²).

1. The ratio does not depend on r, because both forces ∝ 1/r².
2. Ratio = (8.99 × 10⁹ × (1.60 × 10⁻¹⁹)²) / (6.67 × 10⁻¹¹ × (1.67 × 10⁻²⁷)²) = 1.2 × 10³⁶.

Answer: The electric force is about 10³⁶ times larger.

## Check

The distance between two point charges is tripled. The force between them becomes:

- One third
- One ninth
- Three times larger
- Nine times larger

The answer and its explanation are shown in the app once you choose an option.

## Apply it

State one similarity and two differences between gravitational and electric fields.

The model answer is shown in the app after you have tried it.

## Related

- [Gravitational, electric and magnetic fields lesson](https://revise-gray.vercel.app/lesson?subject=wjec-alevel-physics&topic=wjec-alevel-physics.fields)
- [Gravitational, electric and magnetic fields in the library](https://revise-gray.vercel.app/library?topic=wjec-alevel-physics.fields)