Magnetism and induction

Why this matters

Almost all the electricity you use was made by a generator: a coil and a magnet moving relative to each other, turned by steam, water, wind or a gas turbine. The same physics runs electric motors, transformers, induction cooktops, wireless chargers, guitar pickups and MRI scanners. Electrical and mechanical engineers meet it in power systems and machines; physicists and materials scientists meet it in magnetic materials and instruments. This lesson explains the two key facts: currents make magnetic fields, and changing magnetic fields make voltages.

Magnetic fields

A magnetic field B is measured in tesla (T). Some reference sizes:

• Earth's field at the surface: about 25–65 µT (millionths of a tesla).
• A fridge magnet near its surface: a few thousandths of a tesla.
• A hospital MRI scanner: 1.5–3 T.

Field lines leave a magnet's north pole and enter its south pole. Like poles repel and opposite poles attract, but unlike electric charges, magnetic poles always come in pairs: cut a bar magnet in half and you get two smaller magnets.

Moving charges feel magnetic forces

A charge q moving with velocity v through a field B feels a force

F = q · v · B · sin θ

where θ is the angle between v and B. Two things are unusual about this force. It is zero for a charge at rest, and it always acts perpendicular to the motion, so it bends a charge's path without speeding it up. That is how old CRT televisions steered their electron beams and how mass spectrometers sort ions by mass.

A wire carrying current I, with length L inside the field, feels

F = B · I · L · sin θ

That force on current-carrying wires is what turns an electric motor.

Currents make magnetic fields

In 1820 Hans Christian Ørsted noticed that a wire carrying current deflected a compass needle. Every current produces a magnetic field that circles around it. Wind the wire into a coil and the fields from each turn add up, giving a strong field through the middle: an electromagnet. Wrap the coil around iron and the field becomes much stronger still. Relays, door locks, scrapyard cranes and loudspeakers all use electromagnets.

Magnetic flux

To talk about induction we need magnetic flux Φ: how much field passes through a loop.

Φ = B · A · cos θ        units: webers (Wb), 1 Wb = 1 T·m²

A is the loop's area and θ is the angle between the field and the line perpendicular to the loop. Flux is largest when the field passes straight through the loop and zero when the loop is edge-on to the field.

Faraday's law of induction

In 1831 Michael Faraday found that a changing flux through a coil produces a voltage (an electromotive force, emf) around it:

emf = − N · ΔΦ / Δt

N is the number of turns. It does not matter how the flux changes: move a magnet, change the current in a nearby coil, or rotate the coil. A steady flux, however strong, produces nothing.

Example. A 50-turn coil of area 0.010 m² sits in a field that rises from 0 to 0.20 T in 0.10 s:

ΔΦ  = 0.20 × 0.010 = 0.0020 Wb
emf = 50 × 0.0020 / 0.10 = 1.0 V

The minus sign is Lenz's law: the induced current flows in the direction that opposes the change that caused it. Push a magnet toward a coil and the induced current makes a field that pushes back. That opposition is why it takes mechanical work to drive a generator: energy is conserved, and the electrical energy out comes from the work you put in.

How a generator works

1. A coil is turned inside a magnetic field (or a magnet is turned inside a set of coils, as in large power-station generators).
2. As the coil rotates, the angle between the coil and the field changes continuously, so the flux through it rises and falls.
3. The changing flux induces an emf that swings positive and negative in a smooth sine wave: alternating current (AC).
4. One full turn of a simple two-pole generator gives one full AC cycle. The grid frequency is 60 Hz in North America and 50 Hz in most other regions, so a simple two-pole generator must turn 60 (or 50) times per second.

For a coil of N turns and area A spinning at angular speed ω in field B, the peak voltage is

emf_peak = N · B · A · ω

100 turns of area 0.010 m² in 0.50 T, spinning at 60 Hz (ω = 2π × 60 = 377 rad/s), gives a peak of 100 × 0.50 × 0.010 × 377 ≈ 190 V.

A motor is the same machine run backwards: feed it current and the force on the wires turns the shaft.

Transformers

A transformer is two coils wound on a shared iron core. AC in the first coil makes a changing flux in the core, which induces a voltage in the second coil. The voltages scale with the turns ratio:

V_secondary / V_primary = N_secondary / N_primary

Power companies step voltage up for long-distance lines (less current, so less I²R loss in the wires) and step it down near homes. Transformers need a changing flux, which is why the grid uses AC. Grid equipment carries lethal voltages; working on it requires specialist training and authorisation.

Common mistakes

• Expecting a steady field to induce a voltage. Only a change in flux does.
• Forgetting the number of turns. More turns, proportionally more emf.
• Thinking a generator "makes" energy. It converts mechanical work into electrical energy; Lenz's law makes you pay for it.
• Expecting a transformer to work on DC. Steady DC gives a steady flux and no induced voltage.

Quick recap

• B is measured in tesla; moving charges and currents feel magnetic forces.
• Currents create magnetic fields; coils make electromagnets.
• Faraday: emf = −N·ΔΦ/Δt. Lenz: the induced current opposes the change.
• A generator rotates a coil in a field to make AC; a motor is the reverse.
• Transformers change AC voltage by the turns ratio.

Check yourself

This lesson has no coding activity. Use the quiz in the Do tab to check that you can explain how a generator produces a voltage.