Electromagnetic Induction

Electromagnetic induction is how moving magnets and wires can make electricity. When a conductor (like a wire) cuts across magnetic field lines, or when the magnetic field through it changes, an induced e.m.f. (voltage) appears. If the circuit is complete, a current flows.

Key idea

A change in magnetic field linking a conductor makes an e.m.f. Think of magnetic field lines like invisible “traffic lines.” The faster you cut more lines, the bigger the induced e.m.f.

Simple demonstration

Connect a coil to a sensitive meter. Push a bar magnet into the coil: the meter deflects. Pull it out: it deflects the other way. Hold the magnet still: no deflection. This shows that change causes induction, not a steady field.

Factors affecting size of induced e.m.f.

• Speed: move magnet/coil faster → bigger e.m.f.
• Magnetic field strength: stronger magnet → bigger e.m.f.
• Number of turns: more coil turns → bigger e.m.f.
• Orientation: cutting field lines most directly (motion perpendicular to the field) gives the largest e.m.f.

Direction of induced current (Lenz’s law)

The induced current always opposes the change that made it. If you push a magnet into a coil, the coil’s magnetic effect tries to push it back; if you pull the magnet out, the coil’s effect tries to pull it in. This keeps energy conserved.

Relative directions (right-hand rule for generators)

• First finger: magnetic Field (N → S)
• Thumb: Motion of the conductor
• Second finger: induced Current (conventional, + to −)

These three directions are at right angles to each other.

A simple a.c. generator

A coil spins in a magnetic field. As it rotates, the magnetic field through it changes, inducing an e.m.f. Slip rings and brushes connect the spinning coil to the external circuit while allowing it to keep rotating. The output is alternating current (a.c.). The e.m.f. is zero when the coil sides move parallel to the field (cutting no lines), and maximum when they cut the lines most strongly. The graph of e.m.f. against time is a smooth wave with peaks and troughs.

Equations

Definition of e.m.f.:

$$\mathcal{E} = \frac{W}{Q}$$

For induction (idea level):

$$\mathcal{E} \propto \frac{\Delta \Phi}{\Delta t}$$ where $\Phi$ is magnetic flux (how many field lines link the coil).

Common misconceptions

• A strong magnet alone does not induce current; there must be change.
• Current only flows if the circuit is complete; e.m.f. can exist without current.
• Reversing motion or field reverses current direction.