D.2 Electric and magnetic fieldsIB Physics HL: Revision notes

Like charges repel and unlike charges attract. Coulomb's law: F = kq₁q₂/r², with k = 1/(4πε₀) = 8.99 × 10⁹ N m² C⁻². Charge is conserved in an isolated system. Millikan's experiment (balancing an oil drop with qE = mg) showed charge is quantised in units of e = 1.60 × 10⁻¹⁹ C.

Charge is transferred by friction (electrons move between rubbed insulators), by contact (the conductor gets charge of the same sign), and by electrostatic induction. In induction a nearby charged rod separates charge in a conductor; earthing the conductor lets electrons flow to or from earth; removing the earth before the rod leaves a charge opposite to the rod's. In metals only electrons move.

Electric field strength E = F/q, the force per unit charge on a small positive test charge. Field lines start on positive and end on negative charges; line density shows field strength. Between parallel plates the field is uniform: E = V/d. Magnetic field lines form closed loops (bar magnet: N to S outside, S to N inside; straight wire: circles; solenoid: uniform inside).

The electric potential energy Ep of a system is the work done to assemble it from infinite separation. For two point charges, Ep = kq₁q₂/r.

Unlike gravitational Ep, the sign depends on the charges: positive for like charges (work must be done to push them together) and negative for unlike charges (they attract). In the hydrogen atom, Ep ≈ −4.3 × 10⁻¹⁸ J.

The electric potential Ve at a point is the work done per unit charge to bring a small positive test charge from infinity to that point: Ve = kQ/r (volts, J C⁻¹). It is a scalar with zero defined at infinity. It is positive near positive charges and negative near negative charges, and potentials from several charges simply add.

The work done moving a charge q between two points is W = qΔVe, independent of the path.

The field strength is the negative potential gradient: E = −ΔVe/Δr. The field points towards decreasing potential. Between parallel plates V changes linearly with distance, so the gradient, and E, is constant.

Equipotential surfaces join points of equal potential; no work is done moving a charge along one. They are always perpendicular to the field lines. Around a point charge they are concentric spheres; between parallel plates they are planes parallel to the plates. Where equipotentials (for equal steps of V) are close together, the field is strong.