What is a Field? — Quick Summary

Mr Toogood's Physics · Gravitational fields

AQA 3.7.1

F ∝ 1/r²

Both fields

Source ≠ test

Object roles

Mass: attract only

Gravitational

Charge: ± either

Electrostatic

What is a field?

Faraday's iron filings experiment showing magnetic field lines

Faraday's iron filings experiment — one of the earliest ways fields were made visible.

A field is a region of space where an object experiences a non-contact force. First introduced by Michael Faraday to explain forces like electricity and magnetism acting at a distance. Fields are considered physically real — they carry energy and momentum, and propagate at a finite speed (light from the Sun takes ~8 minutes to reach Earth via the electromagnetic field), evidenced directly by effects like radiation pressure.

Source object: creates the field (a mass, a charge, or a moving charge/current).
Test object: interacts with the field itself, not directly with the source.

Field lines & vector representation

A radial field line diagram around a point mass

A radial field around a point mass — field strength falls off as lines spread out.

Fields are vectors — always a size and a direction. Direction is defined as the direction a positive test object would accelerate.

Closer lines = stronger field.
Lines never cross — each point in space has exactly one field direction.
Curved lines: the direction of the force is the tangent to the line at that point.

Radial vs. parallel (uniform) fields

Comparison of a radial field and a parallel uniform field

Radial: strength falls with distance. Parallel: strength stays constant.

Radial: around a point mass, point charge, or a planet — strength decreases with distance (lines spread apart).
Parallel (uniform): e.g. between charged plates, or close to a large body's surface — strength stays constant (lines evenly spaced).

Where fields come from

Source	Field	Notes
Mass	Gravitational	Always attractive
Static charge	Electric	Attract or repel (±)
Moving charge	Magnetic	Stationary charge → none

Gravity is the weakest of the three — we only notice it because Earth's mass is so enormous. At the atomic scale, electric forces completely dominate instead.

Gravitational vs. electric fields

Concept	Gravitational	Electrostatic
Force per...	unit mass (N kg⁻¹)	unit charge (N C⁻¹)
Inverse square	F∝1/r² (Newton)	F∝1/r² (Coulomb)
Attract/repel	Always attracts	Either, by sign

Discovered a century apart (Newton, 1687; Coulomb, 1785), yet both follow an identical inverse-square mathematical form — part of what makes fields such a powerful unifying idea.

Potential energy: a key difference

Gravitational PE is always negative, rising towards zero as separation increases — because gravity is always attractive, work must always be done against it to increase separation. Electric PE can be positive or negative, depending on whether the two charges attract or repel.

The two also differ enormously in strength: in a hydrogen atom, the electrostatic force between the proton and electron is around 10³⁹ times stronger than the gravitational force between them — vast enough that gravity is simply ignored in atomic and particle physics.

Exam essentials

Key similarities

Both inverse-square laws.
Both use field lines, potential, equipotential surfaces.
Identical mathematical form.

Key differences

Mass always attracts; charge can attract or repel.
No negative mass, but charge can be + or −.
G is tiny; electrostatic forces dominate at atomic scale.

Common slips

Don't apply Coulomb's-law reasoning (repulsion) to gravity — it's always attractive.
Gravitational field lines can never diverge from a point the way electric ones sometimes can.
Check the constant (G vs. 1/4πε₀) and sign convention match the field type in the question.