Gravity & Electricity Compared
Gravity & Electricity Compared
- Chapters 13 and 18 are the same mathematics wearing different constants. Examiners test the mapping directly — including the places where it breaks.
The dictionary
| Gravitational | Electric | |
|---|---|---|
| source | mass m | charge Q (either sign) |
| force law | F = GMm/r² | F = Q₁Q₂/4πε₀r² |
| field strength | g = GM/r² (N kg⁻¹) | E = Q/4πε₀r² (N C⁻¹) |
| field defined as | force per unit mass | force per unit positive charge |
| potential | φ = −GM/r, always negative | V = Q/4πε₀r, sign of Q |
| uniform-field version | g near a planet's surface | E = V/d between plates |
| force direction | attraction only | attraction or repulsion |
- The similarity/difference one-liners are banked (9702/42/F/M/23 Q1(c)) (9702/41/M/J/23 Q1(a)(iii)): similarities — both potentials are inversely proportional to distance, both are zero at infinity, equipotentials are concentric spheres; the difference — gravitational potential is always negative, electric potential can be either sign.
Worked example
When both fields act at once (2023 paper)
The Earth (mass kg) carries a charge of C spread evenly over its surface. Using with , find the electric field strength at the surface (9702/41/M/J/23 Q1(c)).
- Both are inverse-square sphere fields, so dividing the two field formulas cancels : .
- .
Answer
The final twist was a direction mark: the charge is negative, so points inward — the same direction as .
How lopsided the two forces are
For two protons in a nucleus, the electric repulsion beats the gravitational attraction by a factor of about . Gravity only wins at planetary scales because matter is electrically neutral overall — the charges cancel, the masses never do. (It also means something stronger than electricity must hold a nucleus together — the strong force, waiting in the Nuclear chapter.)