Module 6 §2: Electric Fields · Year 2
Comparing Electric and Gravitational Fields
Revision notes on Comparing Electric and Gravitational Fields for the OCR A-level Physics specification (H556). Free to read, with 4 practice questions in the app.
The two field types share their entire mathematical structure. Learning them as one pattern with two variations is far more efficient than learning two sets of formulae.
The correspondence
| Gravitational | Electric | |
|---|---|---|
| Source | mass M | charge Q |
| Force | F = GMm/r² | F = Q₁Q₂/(4πε₀r²) |
| Field strength | g = GM/r² | E = Q/(4πε₀r²) |
| Field units | N kg⁻¹ | N C⁻¹ or V m⁻¹ |
| Potential | V = −GM/r | V = Q/(4πε₀r) |
| Potential energy | E = −GMm/r | E = Qq/(4πε₀r) |
| Uniform field | g constant near a surface | E = V/d between plates |
| Field–potential relation | g = −ΔV/Δr | E = −ΔV/Δr |
What is genuinely the same
Both obey inverse square laws for force and field strength, and 1/r laws for potential.
Both have field strength as the negative potential gradient, and potential as a scalar that adds arithmetically.
Both have equipotentials perpendicular to field lines, with no work done along an equipotential.
Both treat spherical bodies as point sources, with r measured centre-to-centre.
What is genuinely different
Two signs versus one. Charge can be positive or negative, so electric forces attract or repel and electric potential can take either sign. Mass has one sign, so gravity only attracts and its potential is always negative.
Shielding. Because charge cancels, an electric field can be screened out — a conducting enclosure has zero field inside it, which is the principle of the Faraday cage. Gravity cannot be shielded by any known means.
Strength. The electrostatic force between two protons exceeds their gravitational attraction by about 10³⁶.
Example: this is the reason gravity governs the universe while electromagnetism governs matter. On the scale of an atom, gravity is so utterly negligible it can be ignored entirely. On the scale of a galaxy, charge has cancelled out so completely that only gravity is left.
A constant that is not universal — G is the same everywhere, but the electric constant depends on the medium: ε₀ applies in a vacuum, and a dielectric increases the permittivity, reducing the force between charges within it.
4 Practice questions on Comparing Electric and Gravitational Fields
Multiple choice and calculations for this topic are in the app, one question at a time. Written answers are marked against the specification and you get the mark scheme with the feedback.
Practise Comparing Electric and Gravitational Fields