Electromagnetism

Syllabus reference

Unit 3, Topic 2 — 23 hours (including practicals)

Coulomb's law

The electrostatic force between two point charges:

Key formula

\[ F = k\frac{q_1 q_2}{r^2} \]

where \(k = \frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\) N m² C⁻²

Like charges repel; unlike charges attract. The force is along the line joining the two charges.

Electric fields

An electric field is a region of space around a charged object within which a force is exerted on other charged objects.

Electric field strength:

\[ E = \frac{F}{q} = k\frac{Q}{r^2} \]

Field lines point away from positive charges and toward negative charges.

Electric potential energy and potential difference

Electrical potential energy is the energy of a charged particle due to its position in an electric field.

Electrical potential difference is the change in electrical potential energy per unit charge:

\[ V = \frac{W}{q} = \frac{\Delta E_p}{q} \]

Equipotential lines join points of equal electrical potential. They are always perpendicular to field lines.

Magnetic fields

A magnetic field is a region of space in which magnetic effects are experienced. Magnetic fields can be produced by permanent magnets or by moving electric charges (electric current).

Field around a current-carrying wire

A long straight current-carrying wire produces a circular magnetic field. Use the right-hand grip rule: thumb points in the direction of conventional current, fingers curl in the direction of the field.

Field strength at distance \(r\) from a long straight wire:

\[ B = \frac{\mu_0 I}{2\pi r} \]

where \(\mu_0 = 4\pi \times 10^{-7}\) T m A⁻¹

Force on a current-carrying conductor

Key formula

\[ F = BIl\sin\theta \]

where \(B\) = magnetic field strength (T), \(I\) = current (A), \(l\) = length of conductor in the field (m), \(\theta\) = angle between conductor and field

Use the right-hand slap rule (or FBI rule) to determine the direction of the force.

Force on a moving charge

\[ F = qvB\sin\theta \]

A charged particle moving perpendicular to a magnetic field follows a circular path (the magnetic force provides the centripetal force).

Electromagnetic induction

Magnetic flux

\[ \Phi = BA\cos\theta \]

where \(\Phi\) = magnetic flux (Wb), \(B\) = field strength (T), \(A\) = area (m²), \(\theta\) = angle between field and normal to area.

Faraday's law

The induced EMF is proportional to the rate of change of magnetic flux:

\[ \varepsilon = -N\frac{\Delta\Phi}{\Delta t} \]

Lenz's law

The induced current flows in a direction that opposes the change in flux that caused it (conservation of energy).

Transformers

\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]

For an ideal transformer: \(V_p I_p = V_s I_s\) (power in = power out).

Simulations and videos

Simulations:

Crash Course Physics:

External resources: