Electricity & Magnetism

Magnets, materials and fields

Every magnet has two poles, north and south, and a simple rule governs them: like poles repel, unlike poles attract. From that one rule the whole of magnetism unfolds.

Poles, forces and materials

A magnet has a north and a south pole. Like poles repel and unlike poles attract. Magnetic materials — iron, steel, cobalt and nickel — are attracted to magnets and can themselves be magnetised; most other materials are non-magnetic.

Temporary and permanent magnets

Soft iron is easily magnetised but loses its magnetism just as easily — ideal for temporary magnets such as electromagnet cores. Steel is harder to magnetise but keeps its magnetism, making it ideal for permanent magnets.

Field lines and plotting

A magnetic field is a region where a magnetic pole feels a force. It is drawn with field lines running from north to south outside the magnet; the direction at any point is the direction of the force on an N pole there. Fields are plotted with a small compass or revealed with iron filings.

Uses of magnets

Permanent magnets are used in compasses, fridge magnets and loudspeakers. Electromagnets — which can be switched on and off — are used in scrapyard cranes, relays, electric bells and many machines.

Electric charge and fields

Charge is the thread running through this chapter. The same two-rule logic as magnetism applies: like charges repel, unlike charges attract.

Charge and charging

There are two kinds of charge, positive and negative. Like charges repel and unlike charges attract. Rubbing two insulators together charges them by friction: only electrons (negative) are transferred — the material that gains electrons becomes negative, the one that loses them becomes positive. Conductors such as metals contain free electrons; insulators do not.

ExtendedElectric fields

An electric field is a region where a charge feels a force; the field direction is the direction of the force on a positive charge. The patterns are radial around a point charge or a charged sphere, and uniform (parallel, evenly spaced lines) between two oppositely charged parallel plates.

Current, e.m.f. and potential difference

An electric current is simply charge on the move. In a metal wire it is a drift of free electrons, driven round the circuit by the cell. A cell does work to push that charge round, and each component takes some of that energy.

Charge in motion

An electric current is a flow of charge, measured by an ammeter connected in series. In metals the current is the movement of free electrons. A direct current (d.c.) flows in one direction; an alternating current (a.c.) repeatedly reverses.

Current is the charge passing a point per unit time: I = Q / t. Conventional current is taken to flow from + to −, while free electrons actually flow from − to +. Worked example: a charge of 30 C passing a point in 10 s gives I = 30 / 10 = 3.0 A.

Driving and using energy

The electromotive force (e.m.f.) of a source is the electrical work it does moving unit charge around a complete circuit. The potential difference (p.d.) across a component is the work done by unit charge passing through it. Both are measured in volts with a voltmeter connected in parallel.

Both are work per unit charge: E = W / Q and V = W / Q. Worked example: a component that transfers 12 J as 2.0 C passes through it has a p.d. of V = 12 / 2.0 = 6.0 V.

Resistance, energy and power

Resistance measures how strongly a component opposes the current. It is found by dividing the p.d. across a component by the current through it.

Measuring resistance

Resistance is found from the p.d. across a component and the current through it: R = V / I. It is measured experimentally with a voltmeter (in parallel) and an ammeter (in series). A longer wire has more resistance; a thicker wire has less.

Resistance is directly proportional to length and inversely proportional to cross-sectional area. Current–voltage graphs reveal each component’s behaviour: a fixed resistor gives a straight line; a filament lamp curves as it heats; a diode conducts in one direction only.

Power, energy and cost

Electrical power is the rate at which a component transfers energy, P = IV; electrical energy is power multiplied by time, E = IVt.

Worked example: a 2.0 kW heater running for 3.0 hours at 15 cents per kW·h uses 2.0 × 3.0 = 6.0 kW·h, costing 6.0 × 15 = 90 cents.

Circuits: symbols, series and parallel

Every circuit diagram is written in a shared language of standard symbols — cell, resistor, variable resistor, lamp, ammeter, voltmeter, switch, thermistor, LDR, diode (Extended), fuse and motor. Reading and drawing them accurately is the foundation of everything in this section.

Two ways to connect

In a series circuit the current is the same everywhere, the p.d.s across components add up to the supply, and the total resistance is the sum: R = R₁ + R₂. In a parallel circuit the source current is shared between branches, every branch has the same p.d., and the combined resistance is less than the smallest branch.

ExtendedCalculating parallel resistance

At any junction the currents in equal the currents out. For two resistors in parallel the combined resistance is found from 1/R = 1/R₁ + 1/R₂. Worked example: two 6.0 Ω resistors in parallel give 1/R = 1/6 + 1/6 = 2/6, so R = 3.0 Ω — less than either resistor.

Potential dividers

Two resistors in series split the supply voltage between them. Swap one for a sensor and the split changes with light or temperature — the basis of an automatic sensing circuit.

Dividing the voltage

Two resistors in series act as a potential divider, sharing the supply voltage in proportion to their resistances. Replacing one with a thermistor or light-dependent resistor makes the output voltage respond to temperature or light, switching a circuit automatically.

For two fixed resistors the voltages divide in the ratio of the resistances: R₁ / R₂ = V₁ / V₂.

Electrical safety

Mains electricity is useful and dangerous in equal measure. Damaged insulation, overheating cables, damp conditions and overloading sockets all risk fire or shock. A handful of safety features stand between a fault and a fire or a shock.

Wiring, fuses and earthing

A mains circuit has a live, a neutral and an earth wire. The switch and fuse are placed in the live wire so the appliance is cut off from the supply when switched off or when a fault occurs. A fuse or trip switch breaks the circuit if the current grows too large; the fuse rating is chosen just above the normal working current.

Earthing and double insulation

An appliance’s outer casing must be either earthed (a metal case connected to earth, so a fault blows the fuse) or double-insulated (a non-conducting case that can never become live). A fuse without an earth wire protects the circuit and cabling of a double-insulated appliance.

Electromagnetism: induction, motors and transformers

Move a magnet near a coil and a voltage appears from nowhere. This is electromagnetic induction — the effect that generates almost all the world’s electricity.

Inducing an e.m.f.

When a conductor cuts magnetic field lines — or the field through a coil changes — an e.m.f. is induced. Pushing a magnet into a coil deflects a sensitive meter; the faster the movement, the more turns on the coil, and the stronger the magnet, the larger the induced e.m.f.

The a.c. generator

An a.c. generator rotates a coil in a magnetic field (or spins a magnet). As the coil cuts field lines it induces an alternating e.m.f., carried to the circuit by slip rings and brushes. The e.m.f. is greatest when the coil moves through the horizontal, cutting lines fastest, and zero as it passes the vertical.

The magnetic effect of a current

A current in a straight wire produces a magnetic field of concentric circles around it. A solenoid produces a field like a bar magnet, with a north and south end. Adding a soft-iron core makes an electromagnet. These are used in relays, where a small current switches a larger circuit, and in loudspeakers.

The field is stronger with a larger current, and its direction reverses when the current direction reverses.

The motor effect and the d.c. motor

A current-carrying conductor in a magnetic field experiences a force. Reversing either the current or the field reverses the force; reversing both leaves it unchanged. The direction is given by Fleming’s left-hand rule. In a d.c. motor, a current-carrying coil in a magnetic field experiences a turning effect, stronger with more turns, a larger current, or a stronger field.

A split-ring commutator, with carbon brushes, reverses the current in the coil every half-turn so that the force on each side always drives the rotation in the same direction. The same motor effect deflects a beam of charged particles moving through a magnetic field.

The transformer

A transformer has a primary and a secondary coil wound on a soft-iron core. More turns on the secondary steps up the voltage; fewer steps down. The voltages are in the same ratio as the turns: Vp/Vs = Np/Ns. Worked example: 1000 primary turns, 50 secondary turns and a 230 V primary give Vs = 230 × 50/1000 = 11.5 V — a step-down transformer.

For an ideal transformer, power in equals power out, so IpVp = IsVs. High-voltage transmission carries the same power at a smaller current, and since power loss in cables is P = I²R, a smaller current means far less energy wasted as heat.