Electricity and magnetism are linked
Until 1820, electricity and magnetism seemed unrelated. That year, Hans Christian Ørsted noticed a compass needle twitch near a current-carrying wire. Within a few decades, Ampère, Faraday and Maxwell showed they are two aspects of one force: electromagnetism.
Magnetic fields
- Magnetic field (B) is measured in teslas (T).
- Earth’s field is about 50 µT (0.000 05 T). A fridge magnet is about 0.005 T. An MRI magnet is 1.5–3 T.
- Field lines go from N to S outside a magnet and never cross.
Fields from currents
Straight wire
A current produces circular field lines around the wire.
Right-hand rule: point your thumb in the direction of conventional current; your fingers curl in the direction of the field.
B = μ₀I ÷ (2πr), where μ₀ = 4π × 10⁻⁷ T·m/A
Solenoid
A coil of wire produces a uniform field inside, like a bar magnet:
B = μ₀nI, where n = turns per metre
Adding an iron core multiplies the field hundreds of times, making a strong electromagnet.
Forces in magnetic fields
The motor effect
A current-carrying wire in a magnetic field feels a force:
F = BIL sin θ
This is the motor effect. Use a right-hand rule (fingers along B, thumb along I, palm pushes in the force direction) to find the direction.
Example: A 0.5 m wire carrying 4 A is perpendicular to a 0.2 T field. F = 0.2 × 4 × 0.5 = 0.4 N.
Moving charges
A charge moving through a field feels F = qvB sin θ. This force is perpendicular to the velocity, so charges move in circles. This principle is used in mass spectrometers, particle accelerators and old TV tubes, and explains why charged particles from the Sun spiral along Earth’s field to create the aurora.
Electric motors
In a DC motor, a current-carrying coil sits in a magnetic field. Forces on opposite sides of the coil push in opposite directions, creating a turning effect. A commutator reverses the current every half turn so the coil keeps spinning the same way.
Electromagnetic induction
Magnetic flux
Magnetic flux: Φ = BA cos θ (unit: weber, Wb)
Faraday’s law
In 1831, Michael Faraday discovered that a changing magnetic flux induces a voltage (EMF) in a coil.
Faraday’s law: ε = −N ΔΦ ÷ Δt
- N = number of turns
- A bigger, faster change gives a larger EMF.
Ways to change the flux: move a magnet, move the coil, change the field strength, change the area, or rotate the coil.
Lenz’s law
Lenz’s law: the induced current flows in a direction that opposes the change in flux that caused it. (That’s the negative sign in Faraday’s law.) It’s a consequence of conservation of energy: you must do work to push a magnet into a coil.
Demonstration: a magnet dropped through a copper pipe falls slowly, because induced currents in the pipe create fields that oppose its motion.
Generators
A generator spins a coil in a magnetic field (or spins magnets past coils). The changing flux induces an alternating EMF.
Nearly all electricity is generated this way: hydro dams, wind turbines, and steam turbines in fossil fuel and nuclear plants. The only major exception is solar photovoltaics.
| Device | Energy conversion |
|---|---|
| Motor | Electrical → kinetic |
| Generator | Kinetic → electrical |
They are essentially the same device run in opposite directions. Electric and hybrid cars use regenerative braking: the motor acts as a generator to recharge the battery.
Transformers
A transformer has two coils wound on an iron core. AC in the primary coil creates a changing flux that induces an EMF in the secondary coil.
V_s ÷ V_p = N_s ÷ N_p
For an ideal transformer, power is conserved: V_pI_p = V_sI_s.
| Type | Turns | Voltage | Current |
|---|---|---|---|
| Step-up | N_s > N_p | Increases | Decreases |
| Step-down | N_s < N_p | Decreases | Increases |
Example: A transformer with 100 primary turns and 2000 secondary turns steps 120 V up to 120 × 20 = 2400 V.
Transformers only work with AC, because DC doesn’t produce a changing flux. Power grids step voltage up to hundreds of kilovolts for transmission (to reduce I²R losses), then step it down for homes.
Other applications
- Induction cooktops: a changing field induces currents directly in the pot.
- Wireless phone chargers: coils in the pad and phone transfer energy by induction.
- MRI scanners: powerful electromagnets and radio waves image the body.
- Maglev trains: magnetic repulsion lifts trains off the track.
- Metal detectors and traffic-light sensors detect induced currents.
Common mistakes
- Thinking a steady magnetic field induces current. Only a changing flux does.
- Thinking transformers create energy. Voltage goes up only as current goes down.
- Using the wrong hand for right-hand rules.
Try it yourself
- A 0.3 m wire carries 5 A at right angles to a 0.8 T field. Find the force.
- A 50-turn coil experiences a flux change of 0.02 Wb in 0.1 s. Find the induced EMF.
- A phone charger reduces 120 V to 6 V. The primary has 400 turns. How many turns are on the secondary?
- Explain why a magnet falls slowly through a copper tube.
(Answers: 1.2 N; 10 V; 20 turns; induced eddy currents create magnetic fields that oppose the magnet’s motion, by Lenz’s law)
Quick recap
- Currents create magnetic fields; right-hand rules give directions.
- F = BIL sin θ is the motor effect.
- Faraday’s law: a changing flux induces an EMF.
- Lenz’s law: induced current opposes the change.
- Generators and transformers rely on induction; transformers work only with AC.