What are the two force laws?

F = Gm_1 m_2r^2 (Newton's law of gravitation)

Two charges of +2.0\,μC and +3.0\,μC are 0.10\,m apart. Find the force between them. Take (1)/(4π_0) = 9.010^9\,N m^2C^-2.

WJEC WJEC 2020-style practice: Calculate the gravitational field strength at the surface of the Earth, given its mass 6.0 × 10^24\,kg and radius 6.4 × 10^6\,m. Take G = 6.67 × 10^-11\,N m^2\,kg^-2. Hence determine the gravitational potential at the surface.

Field strength from g = GM/r^2: g = 6.67 × 10^-11 × 6.0 × 10^24(6.4 × 10^6)^2 = 4.0 × 10^144.1 × 10^13 = 9.8\,N kg^-1. This matches the familiar g at the surface. Gravitational potential from V = -GM/r: V = -6.67 × 10^-11 × 6.0 × 10^246.4 × 10^6 = -6.3 × 10^7\,J kg^-1. Markers reward the field from the inverse-square law giving 9.8\,N kg^-1, and the negative potential from V = -GM/r.

WalesPhysicsSyllabus dot point

How are electric and gravitational fields alike, and how do field strength and potential vary with distance?

Coulomb's law and Newton's law of gravitation, electric and gravitational field strength and potential, and the inverse-square nature of both fields.

A focused answer to WJEC A-Level Physics Unit 4 electrostatic and gravitational fields, covering Coulomb's law and Newton's law of gravitation, electric and gravitational field strength and potential, and the inverse-square nature shared by both fields.

Generated by Claude Opus 4.811 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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What this dot point is asking
The answer
Examples in context
Try this

What this dot point is asking

WJEC wants you to apply Coulomb's law and Newton's law of gravitation, define and use electric and gravitational field strength and potential, and recognise the shared inverse-square structure of the two fields. The parallel between the two fields is one of the most elegant ideas in the course, and the examiners reward students who can map a result from one field onto the other.

The answer

The two force laws

Both are inverse-square laws with the same mathematical form. Gravity is always attractive; the electric force can be attractive or repulsive. The constants differ enormously in strength: gravity is extraordinarily weak between everyday objects, which is why we only notice it when one mass is planet-sized.

Field strength

Potential

The change in potential energy moving between two points is charge (or mass) times the potential difference.

Force between an electron and a proton

In a hydrogen atom the electron and proton are about $5.3 \times 10^{-11}\,\text{m}$ apart, each carrying charge of magnitude $1.6 \times 10^{-19}\,\text{C}$ . Find the electrostatic force. Take $\dfrac{1}{4\pi\varepsilon_0} = 9.0 \times 10^{9}\,\text{N m}^2\,\text{C}^{-2}$ .

step Write Coulomb's law

$F = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q_1 Q_2}{r^2}$ .

step Substitute

$F = 9.0 \times 10^{9} \times \dfrac{(1.6 \times 10^{-19})^2}{(5.3 \times 10^{-11})^2}$ .

step Evaluate

The numerator is $9.0 \times 10^{9} \times 2.56 \times 10^{-38} = 2.3 \times 10^{-28}$ ; dividing by $2.81 \times 10^{-21}$ gives $F = 8.2 \times 10^{-8}\,\text{N}$ , attractive. This is vastly larger than the gravitational pull between the same two particles.

Examples in context

Example 1. An ink-jet printer. Tiny ink droplets are given a charge and then deflected by a uniform electric field between two plates, where the field strength $E = F/Q$ determines the sideways force on each drop. Varying the charge steers each droplet to the right spot on the page. The same field concept that describes a point charge governs this everyday device.

Example 2. Weighing the Earth. Because $g = GM/r^2$ at the surface, measuring the known $g = 9.81\,\text{N kg}^{-1}$ together with the Earth's radius lets you solve for the mass $M$ of the Earth. This is how the planet's mass of about $6 \times 10^{24}\,\text{kg}$ is found without ever placing it on a scale, using only the inverse-square gravitational field.

Try this

Q1. Two charges of $+2.0\,\mu\text{C}$ and $+3.0\,\mu\text{C}$ are $0.10\,\text{m}$ apart. Find the force between them. Take $\frac{1}{4\pi\varepsilon_0} = 9.0\times10^9\,\text{N m}^2\text{C}^{-2}$ . [3 marks]

Cue. $F = \frac{9.0\times10^9\times2.0\times10^{-6}\times3.0\times10^{-6}}{0.10^2} = 5.4\,\text{N}$ (repulsive).

Q2. State one similarity and one difference between gravitational and electric fields. [2 marks]

Cue. Both are inverse-square fields; gravity is always attractive while the electric force can attract or repel.

Exam-style practice questions

Practice questions written in the style of WJEC exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

WJEC 20205 marksCalculate the gravitational field strength at the surface of the Earth, given its mass

6.0 \times 10^{24}\,\text{kg}

and radius

6.4 \times 10^{6}\,\text{m}

. Take

G = 6.67 \times 10^{-11}\,\text{N m}^2\,\text{kg}^{-2}

. Hence determine the gravitational potential at the surface.

Show worked answer →

Field strength from $g = GM/r^2$ :

$g = \dfrac{6.67 \times 10^{-11} \times 6.0 \times 10^{24}}{(6.4 \times 10^{6})^2} = \dfrac{4.0 \times 10^{14}}{4.1 \times 10^{13}} = 9.8\,\text{N kg}^{-1}$ .

This matches the familiar $g$ at the surface.

Gravitational potential from $V = -GM/r$ :

$V = -\dfrac{6.67 \times 10^{-11} \times 6.0 \times 10^{24}}{6.4 \times 10^{6}} = -6.3 \times 10^{7}\,\text{J kg}^{-1}$ .

Markers reward the field from the inverse-square law giving $9.8\,\text{N kg}^{-1}$ , and the negative potential from $V = -GM/r$ .

WJEC 20183 marksState two similarities and one difference between the electric field of a point charge and the gravitational field of a point mass.

Show worked answer →

Similarity one: both field strengths obey an inverse-square law with distance, $E \propto 1/r^2$ and $g \propto 1/r^2$ .

Similarity two: both potentials vary as $1/r$ from the source, and both fields are radial, pointing along the line joining to the source.

Difference: the gravitational force is always attractive, whereas the electric force between charges can be attractive or repulsive depending on the signs of the charges. Markers reward two genuine structural similarities and the attractive-only nature of gravity as the difference.

Related dot points

Sources & how we know this

WJEC A-level Physics specification — WJEC (2015)