Gravitational, Electric and Magnetic Fields Explained: IB Physics Theme D Made Simple
The Moon lifts the oceans without touching them. A magnet moves a paper clip across a gap. Physics explains both with the idea of a field. This guide explains what a field is, which objects create which fields, how to measure how strong a field is, and how gravity and electric force turn out to follow the same inverse-square pattern.
What is a field?
A field is a three-dimensional region around a source where another object experiences a force. The source creates the field. The other object, placed in it, feels the force. A gravitational field is created by a mass and felt by another mass. An electric field is created by a charge and felt by another charge. A magnetic field is created by a moving charge or a magnet and felt by another moving charge or magnet.
Where each field comes from
- •A neutral mass makes a gravitational field only.
- •A charged mass makes a gravitational field and an electric field.
- •A moving charged mass (a current) makes all three: gravitational, electric and magnetic fields.
Field strength and its units
Field strength is the force on each unit of the thing that feels the field:
- •Gravitational field strength g = F ÷ m, in newtons per kilogram. A 2.0 kg mass feeling 20 N has g = 10 N/kg, pointing toward the source.
- •Electric field strength E = F ÷ q, in newtons per coulomb. The direction is that of the force on a positive test charge.
- •Magnetic field strength B = F ÷ (qv) = F ÷ (IL), in tesla (N A⁻¹ m⁻¹), with the force at right angles to both the field and the motion.
The direction rules
- •The gravitational field points toward the mass, because gravity only attracts.
- •The electric field points away from a positive charge and toward a negative charge, the way a positive test charge would be pushed.
- •The magnetic field points the way the north pole of a compass points.
Two laws with the same shape
Newton’s law of gravitation: F = GMm ÷ r², always attractive, with G = 6.67 × 10⁻¹¹ N m² kg⁻². Coulomb’s law: F = kQq ÷ r², attractive for unlike charges and repulsive for like charges, with k = 8.99 × 10⁹ N m² C⁻². Dividing by the test object gives the fields of a point source: g = GM ÷ r² and E = kQ ÷ r².
Both are inverse-square laws: double the distance and the force or field falls to a quarter. For a sphere, r is measured from the centre. At a height equal to the Earth’s radius above the surface, r is 2R and g falls to 9.8 ÷ 4 = 2.5 N/kg, a classic slip when students use R instead of 2R.
Two worked comparisons
- •The Earth (5.97 × 10²⁴ kg) and the Moon (7.35 × 10²² kg), 3.84 × 10⁸ m apart: F = GMm ÷ r² = 1.98 × 10²⁰ N.
- •The electron and proton in a hydrogen atom, 5.3 × 10⁻¹¹ m apart: the electric force is 8.2 × 10⁻⁸ N and the gravitational force is 3.6 × 10⁻⁴⁷ N. The electric force is about 10³⁹ times bigger, which is why gravity is negligible between charged particles.
Magnetic force between two wires
Two long parallel wires carrying currents I₁ and I₂, a distance r apart, attract each other when the currents flow the same way and repel when they flow in opposite directions. The force on each metre is F ÷ L = μ₀I₁I₂ ÷ 2πr, with μ₀ = 4π × 10⁻⁷ T m/A. For two 10 A currents 5.0 cm apart that is 4.0 × 10⁻⁴ N per metre.
Frequently asked questions
Gravitational fields come from mass and only attract, with g = GM ÷ r². Electric fields come from charge and can attract or repel, with E = kQ ÷ r². Both fall off as 1 ÷ r².
B = F ÷ (qv) for a charge q moving at speed v at right angles to the field, or B = F ÷ (IL) for a length L of wire carrying current I. The unit is the tesla.
g is in newtons per kilogram (N/kg) and E is in newtons per coulomb (N/C). They are both force per unit mass or charge.
Currents in the same direction attract. Currents in opposite directions repel. This is the opposite of the pattern for like charges.