Electric and magnetic fields

📚The physics

Coulomb’s law

is Newton’s law of gravitation with charge in place of mass — same inverse square, same centre-to-centre distance. The difference that matters is that charge comes in two signs, so the electric force can repel as well as attract, while gravity only ever attracts. Almost every asymmetry between the two field types traces back to that one fact.

The other difference is scale. Between two protons the electric repulsion is about \( 10^{36} \) times the gravitational attraction. Gravity dominates the universe only because large bodies are electrically neutral.

Electric field strength \( E = F/q = kQ/r^{2} \) is force per unit positive charge, so field lines point away from positive charges and towards negative ones. They start on positive, end on negative, never cross, and are always perpendicular to conductor surfaces.

Between parallel plates the field is uniform, \( E = V/d \), with evenly spaced parallel lines except for the fringing at the edges. This is the arrangement used to accelerate and deflect charged particles, and it reappears in D.3.

Magnetic fields are produced by moving charge — there are no magnetic monopoles, so field lines always form closed loops. Three patterns to know cold: around a bar magnet, out of the north pole and round to the south; around a straight wire, concentric circles whose direction is given by the right-hand grip rule with the thumb along the conventional current; inside a solenoid, uniform and parallel, looking like a bar magnet from outside.

Force on a current. \( F = BIL\sin\theta \), where \(\theta\) is the angle between the current and the field. Note that a wire parallel to the field feels no force at all. Direction comes from Fleming’s left-hand rule: first finger field, second finger current, thumb motion. This is the motor effect, and it is the reason a loudspeaker cone moves.

HLElectric potential and potential energy

\( V_e = kQ/r \) and \( E_p = kQ_1Q_2/r \). Unlike the gravitational versions these are not always negative: two like charges have positive potential energy, because they would fly apart if released, while opposite charges have negative potential energy and are bound. Getting the sign right is usually the whole difficulty.

HLGravitational versus electric

The comparison table is worth building yourself, because examiners ask for it directly.

Both are inverse-square forces with inverse-\(r\) potentials; gravity is always attractive and always negative in potential, while electricity does both. And the constants differ by forty orders of magnitude.