Electricity and magnetism

📚The physics

Magnetism. Like poles repel, unlike poles attract. Field lines run from north to south outside a magnet, never cross, and are closest together where the field is strongest. A permanent magnet keeps its magnetism; an induced magnet only behaves as one while it is in a field. Magnetic materials are iron, steel, cobalt and nickel — not all metals, so aluminium and copper are not attracted. Soft iron magnetises and demagnetises easily, which makes it right for electromagnet cores; steel holds its magnetism, which makes it right for permanent magnets.

Current and charge. Current is the rate of flow of charge, \( I = Q/t \). Conventional current flows from + to −, opposite to the electrons. E.m.f. is the energy given to each coulomb by the supply; potential difference is the energy delivered by each coulomb to a component. Same unit, different jobs.

Resistance is \( R = V/I \). For a wire, resistance increases with length and decreases with cross-sectional area — a long thin wire resists most. Energy and power come from \( E = IVt \) and \( P = IV \), and with \( V = IR \) you can also write \( P = I^{2}R \).

Series circuits: one path, so the current is the same everywhere, the potential differences add up to the supply, and total resistance is the sum. Parallel circuits: several paths, so the potential difference across each branch is the same, the branch currents add up to the total, and the combined resistance is less than the smallest branch.

A thermistor has a resistance that falls as temperature rises; an LDR has a resistance that falls as light gets brighter. Put either in a potential divider and you have a sensor circuit.

Electrical safety. A fuse is a thin wire that melts if the current gets too large, breaking the circuit — it must be fitted in the live wire, otherwise the appliance stays live even after the fuse blows. Earthing gives a fault current a safe path so a metal case can never become live. A circuit breaker does the fuse’s job but can be reset. Double insulation means the appliance has no exposed metal, so it needs no earth wire. The main hazards are damaged insulation, overheating cables, damp conditions and overloaded sockets.

Electromagnetic effects. A current in a wire creates a magnetic field — circles round a straight wire, and a bar-magnet pattern in a solenoid. Conversely, moving a magnet near a coil induces an e.m.f., and the induced current always opposes the change causing it. Nothing is induced if nothing moves.

The a.c. generator spins a coil in a magnetic field, producing an alternating e.m.f. that peaks when the coil is parallel to the field and is zero when it is perpendicular — because the rate of change of field through the coil is what matters, not the field itself.

The motor effect is the force on a current-carrying wire in a magnetic field, direction from Fleming’s left-hand rule. Give a coil a commutator and you have a d.c. motor.

Transformers change voltage:

They work on alternating current only, because a steady current produces no changing field and so induces nothing. In an ideal transformer power is conserved, so stepping voltage up steps current down. This is why electricity is transmitted at very high voltage — lower current means far less energy wasted heating the cables, since that loss goes as \( I^{2}R \).