Electromagnetic induction: Faraday's and Lenz's laws: WASSCE Physics

Move a magnet into a coil and a current appears from nowhere — no battery needed. Faraday's discovery of electromagnetic induction is how almost all the world's electricity is generated, from Bumbuna's turbines to a bicycle dynamo.

Learning objectives

By the end of this lesson you should be able to:

describe experiments showing electromagnetic induction
state Faraday's and Lenz's laws of electromagnetic induction
use Fleming's right-hand rule to find the direction of an induced current
state the factors affecting the size of the induced e.m.f.

Electromagnetic induction

A bar magnet being pushed into a coil connected to a galvanometer; the galvanometer deflects while the magnet moves

Figure 1. Inducing a current by moving a magnet into a coil. WASSCE Tutor diagram.

Definition

Electromagnetic induction is the production of an e.m.f. (and a current, if the circuit is complete) in a conductor when the magnetic flux linking it changes.

Observations with a magnet and a coil connected to a galvanometer:

Action	Galvanometer
magnet pushed into the coil	deflects one way
magnet held still inside the coil	no deflection
magnet pulled out	deflects the opposite way
magnet moved faster	larger deflection
stronger magnet, or coil with more turns	larger deflection

The same happens if the coil is moved instead of the magnet: what matters is relative motion — a changing magnetic field through the coil.

A straight wire moved across a magnetic field (cutting the field lines) also has an e.m.f. induced in it.

Faraday's law

Definition

Faraday's law of electromagnetic induction: the magnitude of the induced e.m.f. is directly proportional to the rate of change of magnetic flux linking the circuit:

E = -N\dfrac{\Delta\Phi}{\Delta t}

Here Φ is the magnetic flux (in webers, Wb; $\Phi = BA$ for a flux density $B$ through an area $A$ at right angles), and $N$ the number of turns.

Factors affecting the induced e.m.f.

the speed of relative motion (rate of change of flux)
the strength of the magnetic field
the number of turns on the coil
the area of the coil

Worked example

The flux through a coil of 200 turns changes from 0.004 Wb to 0.001 Wb in 0.1 s. Find the average induced e.m.f.

E = N\dfrac{\Delta\Phi}{\Delta t} = 200 \times \dfrac{0.004 - 0.001}{0.1} = 200 \times 0.03 = 6\ \text{V}

\begin{aligned}E &= N\dfrac{\Delta\Phi}{\Delta t} \\ &= 200 \times \dfrac{0.004 - 0.001}{0.1} \\ &= 200 \times 0.03 \\ &= 6\ \text{V}\end{aligned}

For a straight conductor of length $L$ moving at speed $v$ at right angles to a field $B$ :

E = BLv

Worked example

A rod 0.5 m long moves at 4 m s⁻¹ at right angles to a magnetic field of 0.2 T. Find the e.m.f. induced across its ends.

E = BLv = 0.2 \times 0.5 \times 4 = 0.4\ \text{V}

\begin{aligned}E &= BLv \\ &= 0.2 \times 0.5 \times 4 \\ &= 0.4\ \text{V}\end{aligned}

Lenz's law

Definition

Lenz's law: the direction of the induced current is always such as to oppose the change producing it.

When the N pole of a magnet is pushed into a coil, the induced current makes that end of the coil a N pole, which repels the approaching magnet. When the magnet is pulled out, that end becomes a S pole, attracting it back. Either way, you must do work against the opposing force — and that work becomes the electrical energy. Lenz's law is the conservation of energy in electromagnetism (the minus sign in Faraday's law).

Fleming's right-hand rule

Definition

Fleming's right-hand rule (the dynamo rule): hold the thumb, first finger and second finger of the right hand mutually at right angles. If the thuMb points in the direction of Motion of the conductor and the First finger along the Field (N → S), the seCond finger gives the direction of the induced Current.

Common mistake

Left hand for motors (force on a current), right hand for generators (induced current). A memory aid: "Generators are Right" (dynamo — right; motor — left).

Key points

A changing magnetic flux through a circuit induces an e.m.f.; no change, no e.m.f.
Faraday: e.m.f. ∝ rate of change of flux; $E = N\dfrac{\Delta\Phi}{\Delta t}$ , $E = BLv$ .
Lenz: the induced current opposes the change causing it (conservation of energy).
Fleming's right-hand rule gives the direction of the induced current.

WASSCE examination focus

WAEC tests this

Describe an experiment demonstrating electromagnetic induction, state Faraday's and Lenz's laws, give the factors affecting the induced e.m.f., and explain how Lenz's law follows from the conservation of energy. Calculations with $E = N\Delta\Phi/\Delta t$ and $E = BLv$ appear in theory papers.

Quick check

What happens to the galvanometer when a magnet is held still inside a coil?
State Lenz's law.
Find the e.m.f. induced in a 0.4 m wire moving at 5 m s⁻¹ across a 0.1 T field.

Answers: 1. Nothing: there is no deflection because the flux is not changing. 2. The induced current flows in a direction that opposes the change producing it. 3. $E = 0.1 \times 0.4 \times 5 = 0.2$ V.

Electromagnetic induction: Faraday's and Lenz's laws

Learning objectives

Electromagnetic induction

Faraday's law

Factors affecting the induced e.m.f.

Lenz's law

Fleming's right-hand rule

Key points

WASSCE examination focus

Quick check

Keep going with electromagnetic induction

More lessons in Electromagnetic Induction