When a magnetic field changes around a conductor, it creates an electric voltage (emf) in that conductor. Think of a magnet sliding under a coil of wire – the magnet’s motion “pushes” electrons in the wire, making them flow. This is the basis of generators, transformers and many everyday devices.
Faraday discovered that the induced emf is proportional to the rate of change of magnetic flux through the circuit.
| Symbol | Meaning |
|---|---|
| \$E\$ | Induced electromotive force (voltage) |
| \$N\$ | Number of turns in the coil |
| \$\Phi\$ | Magnetic flux (\$\Phi = B A \cos\theta\$) |
\$E = -N \frac{d\Phi}{dt}\$
Key point: The negative sign is not a mistake – it tells us the direction of the induced emf (see Lenz’s Law below).
A magnet moves through a coil at a constant speed. The magnetic flux changes at a constant rate, so the induced emf is constant. If the magnet moves twice as fast, the emf doubles.
Lenz’s Law says the induced current always flows so that its magnetic field opposes the change that produced it. In other words, the system resists the change.
This opposition is why the negative sign appears in Faraday’s equation.
Remember: The negative sign in Faraday’s law comes from Lenz’s Law. It tells you the direction of the induced emf and current.
Diagram practice: Draw a magnet and coil, label the direction of the magnetic field, and use the right‑hand rule to find the induced current direction.
Units: emf is in volts (V), magnetic flux in webers (Wb), time in seconds (s). Check that your equations keep the units consistent.
Common pitfalls: Mixing up the sign of \$d\Phi/dt\$ or forgetting the number of turns \$N\$ can lead to wrong answers. Double‑check each step.