recall and use Faraday’s and Lenz’s laws of electromagnetic induction
Electromagnetic Induction ⚡️
What is Electromagnetic Induction?
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’s Law of Induction 🔄
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).
Quick Example
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 – The Direction of Induced Current 🧲
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.
- Magnet moves towards the coil → induced current creates a magnetic field that pushes the magnet away.
- Magnet moves away from the coil → induced current creates a magnetic field that pulls the magnet back.
This opposition is why the negative sign appears in Faraday’s equation.
Practical Applications 🎛️
- Electric generators – turning a coil in a magnetic field to produce electricity.
- Transformers – changing voltage levels using two coils with a shared magnetic core.
- Induction cooktops – heating metal pots via alternating magnetic fields.
- Magnetic brakes – using induced currents to slow down trains.
Exam Tips & Tricks 📝
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.
Revision
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