Physics › Electric fields › Comparing electric and gravitational fields
Comparing electric and gravitational fields
Set the two field theories side by side and the equations match line for line, the same mathematics written twice with different constants. The differences are that charge comes in two signs while mass comes in one, and that between two protons the electrostatic repulsion is about 10³⁶ times the gravitational attraction.
Pick your board and the few notes written for the other boards quietly fold away, here and in the practice players. Nothing is deleted: every folded piece reopens on a tap.
Builds on Electric potential and Newton's law of gravitation.
IN THIS TOPIC
- Pair the gravitational and electric equations, and state the one structural difference between them.
- Compare the magnitudes of the two forces between subatomic particles, and interpret the answer.
COMMON MISCONCEPTION
Gravity is the strongest force.
The formula ladder, reused
Every tool the gravity unit built reappears here with the cast changed. G becomes 1/4πε0, mass becomes charge, and each equation keeps its shape. Both are inverse-square laws, and that shared mathematics is what brings both the same apparatus of field lines, potential and equipotential surfaces. The minus signs mark the one asymmetry. Gravitational potential is always negative, since gravity only ever attracts, while electric potential takes the sign of its charge. The booklet then prints g = −ΔV/Δr with its sign but quotes the electric E = ΔV/Δr as a magnitude.
The structural difference
Masses always attract. Charges may attract or repel, because charge comes in two signs and mass comes in one. That asymmetry determines which force dominates on which scale. Bulk matter is almost perfectly neutral, its positive and negative charges cancelling to fantastic precision, so the electric force, for all its strength, largely switches itself off over large scales. Mass has no cancelling partner. Every kilogram adds and nothing subtracts, so an unshieldable attraction that can only accumulate ends up sculpting planets, stars and galaxies by default.
GUIDED PRACTICE
Whose field is this?
A field-line diagram shows lines pointing radially inward to a central dot. Give two different physical situations it could represent, and the single feature that distinguishes their sources.
Show the working
It is the field of any mass, since gravity only attracts, or of a negative point charge, whose lines run inward by the positive-test-charge convention.
The distinguishing feature is the sign choice electricity enjoys and gravity lacks. Reverse the charge and the same diagram flips outward; no mass in the universe can make gravity's lines do that.
Two protons settle it
The comparison between subatomic particles is asked for directly, and two protons inside a nucleus make the cleanest case. At a separation of 1.0 fm the electric repulsion comes to about 230 N, a startlingly human-sized force on a particle of 10−27 kg, while the gravitational attraction between the same pair is about 1.9 × 10−34 N. Their ratio sits near 1036, independent of separation, since both forces carry the same 1/r2. Particle physics therefore ignores gravity outright. Something stronger still, the strong nuclear force from the particles unit, has to exist to hold nuclei together against that 230 N of repulsion.
ASSESSMENT FOCUS
- The comparison question has a fixed skeleton. Similarities are the inverse-square law and the shared structure of field lines, potential and equipotentials; the difference is attract-only against attract-or-repel. Give both halves.
- For the proton calculation, take both masses and both charges from the data booklet and keep r identical in the two laws. Present the answer as a ratio near 1036. That ratio needs no value of r at all, since both laws carry 1/r2 and it cancels, and saying so is usually worth a mark on its own.
- “Why does gravity dominate astronomy?” wants the cancellation argument. Matter is neutral, so electric forces cancel, while masses only add and gravity cannot be screened.
- One cross-topic link is worth making here. The 230 N of repulsion inside a nucleus is exactly what the strong force has to beat, which ties this unit straight back to particle physics.
CHECK YOURSELF
Two protons sit 1.0 fm apart. Using data-booklet values, find the electric and gravitational forces between them and the ratio of the two. Why, despite this ratio, does gravity and not electricity shape galaxies?
Show a hint
Same r in both laws, so the ratio outlives it.
Show the answer
Electric: = (8.99 × 109 × (1.60 × 10−19)2) / (1.0 × 10−15)2 ≈ 230 N, repulsive.
Gravitational: = (6.67 × 10−11 × (1.67 × 10−27)2) / (1.0 × 10−15)2 ≈ 1.9 × 10−34 N.
Ratio ≈ 1.2 × 1036, independent of r. Galaxies still belong to gravity because bulk matter is neutral, so charges cancel and electric forces screen themselves out, while masses only ever add.
One inverse-square shape, two casts of characters. Electricity wins by 10³⁶, and neutrality still hands the universe to gravity.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
Or read them with their mark schemes on the comparing electric and gravitational fields questions page.
WHERE TO GO NEXT
- Proportional reasoning is the maths this lesson leans on, worked through from GCSE.
CHECK YOUR PROGRESS
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- Pair the gravitational and electric equations, and state the one structural difference between them.
- Compare the magnitudes of the two forces between subatomic particles, and interpret the answer.
Open the full revision checklist to track your progress across the whole unit.