Electromagnetic Induction

4.5.1 Direction of Induced EMF

Objective: Know that the direction of an induced e.m.f. opposes the change causing it.

Faraday's Law of Induction

Faraday's Law describes the magnitude of the induced electromotive force (e.m.f.) in a closed circuit. It states that the magnitude of the induced e.m.f. is proportional to the rate of change of magnetic flux through the circuit.

Mathematically, this is represented as:

$$ \mathcal{E} = - \frac{N \Delta \Phi}{\Delta t} $$

Where:

• $\mathcal{E}$ is the induced e.m.f. (in volts)
• $N$ is the number of turns in the coil
• $\Delta \Phi$ is the change in magnetic flux (in Weber)
• $\Delta t$ is the time interval over which the change in flux occurs (in seconds)

The negative sign indicates that the direction of the induced e.m.f. opposes the change in magnetic flux. This is known as Lenz's Law.

Lenz's Law

Lenz's Law provides the direction of the induced e.m.f. It states that the direction of the induced current is such that it opposes the change in magnetic flux that produced it.

This can be visualized using a right-hand rule:

1. Point your fingers in the direction of the changing magnetic flux.
2. Your thumb will point in the direction of the induced current.

Examples

Here are some examples illustrating Lenz's Law:

1. Moving a magnet towards a coil: The induced current will create a magnetic field that repels the approaching magnet.
2. Moving a magnet away from a coil: The induced current will create a magnetic field that attracts the receding magnet.
3. Changing the current in a coil: The changing current will create a magnetic field that opposes the change in the original current.

Table Summary

Concept	Description
Faraday's Law	The induced e.m.f. is proportional to the rate of change of magnetic flux.
Lenz's Law	The direction of the induced current opposes the change in magnetic flux.
Mathematical Representation	$\mathcal{E} = - \frac{N \Delta \Phi}{\Delta t}$