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

> define electric and gravitational potential and relate field strength to potential gradient

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Specification statement (Unit 3.4(c)): define electric and gravitational potential and relate field strength to potential gradient

## Explanation

1. **Potential** at a point is the work done per unit mass (gravitational) or per unit positive charge (electric) in bringing it from infinity to that point.
2. Gravitational potential V = −GM/r is always negative (zero at infinity, attractive force). Electric potential V = Q/(4πε₀r) has the sign of Q.
3. Field strength is the negative **potential gradient**: g = −ΔV/Δr, E = −ΔV/Δx. Equipotentials are always perpendicular to field lines; no work is done moving along one.

## Worked example

How much energy is needed to move a 1000 kg probe from the Earth's surface (V = −62.5 MJ kg⁻¹) to an orbit where V = −58.1 MJ kg⁻¹?

1. ΔV = −58.1 − (−62.5) = +4.4 MJ kg⁻¹.
2. Energy = mΔV = 1000 × 4.4 × 10⁶ = 4.4 × 10⁹ J.

Answer: 4.4 × 10⁹ J (ignoring the kinetic energy needed for orbit).

## Check

Why is gravitational potential always negative?

- Gravity points downwards
- Zero is at infinity, and work must be done against the attraction to get there
- Mass can be negative
- It is a convention with no reason

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

## Apply it

The potential falls by 120 V over 0.030 m in a uniform field. Calculate the field strength and state its direction.

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)