Physics › Electric fields › Comparing electric and gravitational fields

Comparing electric and gravitational fields

Every gravitational equation has an electric twin of the same form, with charge for mass and 1/4πε₀ for G, and both are inverse square laws. Charge has two signs and mass has one, so electric forces can repel while gravity cannot. Between two protons the electric repulsion is about 10³⁶ times the gravitational attraction, whatever their separation.

Comparing electric and gravitational fields

Watch on YouTube (opens in a new tab)

Year 13AQA 3.7.1, 3.7.3.1OCR A 6.2.2(c)EDEXCEL 179

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.

Gravity is by far the weaker force: between two protons, electric repulsion exceeds gravitational attraction by about 10³⁶. Gravity dominates on large scales only because bulk matter is electrically neutral.

The matching equations

A two-column ladder pairing the gravitational and electric formulas row by row: force, field strength, potential, and the size of the potential gradient, identical in shape, with q the test charge, Q the source charge, and only gravity's potential carrying a minus sign.
FIG. 1Force, field strength, potential and potential gradient, paired between the two theories: four rows of the same algebraic form. The gradient row is written in magnitudes, g = |ΔV/Δr| and E = |ΔV/Δr|, with q the test charge and Q the source charge.

Each equation from the gravity unit has an electric counterpart of the same form: G is replaced by 1/4πε0 and mass by charge. Both forces follow inverse-square laws, and that shared mathematics is why both use the same apparatus of field lines, potential and equipotential surfaces. The minus signs mark the one asymmetry: gravitational potential is always negative, because gravity only attracts, while electric potential takes the sign of its source charge. The booklet 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 has two signs and mass has one. That difference determines which force dominates on which scale. Bulk matter is very nearly neutral, its positive and negative charges cancelling to high precision, so on astronomical scales the electric force largely cancels out despite its strength. Mass does not cancel: gravitational fields cannot be screened, and although the fields of different masses can cancel at a particular point, a large body's contributions add, so gravity is the dominant force on the scale of planets, stars and galaxies.

GUIDED PRACTICE

Identifying the source of a radial field

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 that charge has two signs and mass has one. Reversing the sign of the charge reverses the field lines, whereas no mass produces an outward gravitational field.

The two forces between two protons

Two protons a femtometre apart with both forces quoted: an electric repulsion of two hundred and thirty newtons against a gravitational attraction of ten to the minus thirty-four newtons, a ratio of ten to the thirty-six.
FIG. 2Both forces between two protons a femtometre apart: 230 newtons of electric repulsion against 10⁻³⁴ newtons of gravity.

The comparison between subatomic particles is examined directly, and two protons in a nucleus are the standard case. At a separation of 1.0 fm the electric repulsion is about 230 N, acting on a particle of mass of order 10−27 kg, while the gravitational attraction between the same pair is about 1.9 × 10−34 N. The ratio is about 1036 and is independent of separation, because both forces vary as 1/r2. Gravity is therefore neglected in particle physics. A stronger interaction, the strong nuclear force covered in the particles unit, is needed to hold nuclei together against that 230 N of repulsion.

ASSESSMENT FOCUS

  • The comparison question has a fixed structure: the similarities are the inverse-square law and the shared apparatus of field lines, potential and equipotentials; the difference is that gravity only attracts while electric forces may attract or repel. Give both halves.
  • For the proton calculation, take both masses and both charges from the data booklet and use the same r in both laws. Present the answer as a ratio of about 1036. The ratio does not require a value of r, since both laws contain 1/r2 and it cancels, and stating that carries credit.
  • “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.
  • The 230 N of repulsion inside a nucleus is the force the strong nuclear force must exceed, which links this unit 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

Use the same r in both laws; it cancels from the ratio.

Show the answer

Electric: F=Q1Q2/4πε0r2F = Q_{1}Q_{2}/4\piε_{0}r^{2} = (8.99 × 109 × (1.60 × 10−19)2) / (1.0 × 10−15)2 ≈ 230 N, repulsive.

Gravitational: F=Gm2/r2F = Gm^{2}/r^{2} = (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. Gravity nevertheless determines the structure of galaxies because bulk matter is neutral, so electric forces cancel, whereas gravitational attraction cannot be screened and the contributions of many masses add.

Both forces follow inverse-square laws. Between two protons, the electric force is about 10³⁶ times stronger than gravity; on astronomical scales, electrical neutrality leaves gravity dominant.

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.

Question workbook

PDF · 58 KB · print edition · white background

Question workbook

PDF · 58 KB · screen edition · navy

Answer book

PDF · 58 KB · fully worked · navy
18 questions on this topicAnswer them one at a time and mark yourself against the mark scheme.Practise this topic

Or read them with their mark schemes on the comparing electric and gravitational fields questions page.

4 flashcards on this topicDefinitions, off-sheet equations and a spot-the-error card, scheduled by spaced repetition in your browser.Revise with flashcards

WHERE TO GO NEXT

CHECK YOUR PROGRESS

Rate how confident you feel with each objective for this lesson. Ratings are saved in this browser, on this device, unless you sign in.

  • 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.