Electromagnetic Induction

Overview

Electromagnetic induction is the production of an induced emf, and an induced current if the circuit is complete, when the magnetic flux linkage changes through a conductor or coil.

This topic is a major link between magnetism and electricity, and underpins electric power generation, transformers, microphones, pickups, braking systems, and many sensing devices.

A key exam idea:

Induction does not occur simply because a magnetic field is present. Induction requires changing magnetic flux linkage.

Core Ideas

Electromagnetic-induction questions revolve around a few linked ideas:

• magnetic flux measures how much field passes through a surface
• magnetic flux linkage includes the number of turns in a coil
• induced emf depends on the rate of change of flux linkage
• Lenz’s law determines direction by opposing the change
• induction can be produced by changing field strength, area, orientation, or relative motion
• eddy currents are a bulk-conductor consequence of changing flux

Exam Relevance

Students are expected to:

• use the correct angle in $\Phi =BA\cos \theta$
• distinguish flux from flux linkage
• apply Faraday’s law in sign and magnitude form
• use Lenz’s law systematically for current direction
• interpret flux-time and emf-time graphs
• recognise when induction does or does not occur

Prior Links Between Electricity and Magnetism

Earlier topics established that:

• electric currents produce magnetic fields
• magnetic fields exert forces on moving charges and currents

See:

• Current Electricity Fundamentals
• Magnetic Fields
• Magnetic Force

Electromagnetic induction completes the connection:

• changing magnetic conditions can produce emf and current

Key Representations

Magnetic Flux

Definition

Magnetic flux $\Phi$ measures how much magnetic field passes through a surface.

For a uniform field:

$$\Phi =BA\cos \theta$$

where:

• $B$ = magnetic flux density
• $A$ = area of surface
• $\theta$ = angle between the magnetic field and the area normal

Angle Convention

This is one of the most common mistakes.

• $\theta$ is measured between the field direction and a line perpendicular to the surface
• if the angle to the plane is given, convert first

Maximum and Zero Flux

• maximum flux when field is perpendicular to the surface:

$$\theta =0^{\circ },\Phi =BA$$

• zero flux when field is parallel to the surface:

$$\theta =90^{\circ },\Phi =0$$

Unit

$$1\text{Wb}=1{\text{T m}}^2$$

Visual Reference

Figure: Magnetic flux through a surface depends on the perpendicular component of the magnetic field. The angle is taken relative to the surface normal, not the plane itself.

Magnetic Flux Linkage

For a coil with $N$ turns:

$$N\Phi$$

This is magnetic flux linkage.

Factors Affecting Flux Linkage

$$N\Phi =NBA\cos \theta$$

So flux linkage changes if any of the following changes:

• number of turns $N$
• magnetic field strength $B$
• area $A$
• orientation $\theta$

Faraday’s Law

The induced emf equals the negative rate of change of magnetic flux linkage:

$$\mathcal{E}=-\frac{d(N\Phi )}{dt}$$

Average form:

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

Meaning

Larger induced emf occurs when:

• flux linkage changes more rapidly
• a stronger field is used
• more turns are used
• a larger area is used
• faster rotation or motion occurs

Lenz’s Law

The induced current flows in a direction such that its magnetic effects oppose the change causing it.

This explains the negative sign in Faraday’s law.

Do not memorise the minus sign mechanically.

Why It Must Oppose Change

If the induced current assisted the change, energy would be created without input. This would violate conservation of energy.

Direction of Induced Current

General method:

1. Decide whether magnetic flux linkage is increasing or decreasing.
2. The induced field must oppose that change.
3. Determine the induced field direction.
4. Use the right-hand grip rule to determine current direction.

Ways to Produce Induction

Any method that changes flux linkage can induce emf.

1. Move Magnet or Coil

• magnet towards coil
• magnet away from coil
• coil entering or leaving field

2. Rotate Coil

Changes angle $\theta$ continuously.

3. Change Coil Area

Flexible loop expanding or shrinking.

4. Change Magnetic Field Strength $B$

Increase or decrease electromagnet current.

5. Nearby Changing Current

Changing current in one coil changes the field through another coil.

Experimental Observations

Faster Motion Gives Larger emf

Move a magnet faster towards a coil:

• larger rate of change of flux
• larger galvanometer deflection

Reverse Motion Reverses Current

Moving a magnet away instead of towards the coil reverses induced current direction.

Switching Nearby Coil On or Off

When current in a nearby coil changes:

• magnetic field changes
• induced emf appears in the second coil

A steady current gives no induction after the field becomes constant.

Motional emf Overview

If a conductor of length $l$ moves through a magnetic field at speed $v$:

$$\mathcal{E}=Blv$$

This is due to magnetic force on charges causing charge separation.

See Motional emf.

Alternating Current Generators Overview

A rotating coil in a magnetic field experiences continuously changing flux linkage, producing alternating emf.

Key features:

• sinusoidal output
• mechanical energy converted to electrical energy
• depends on rotation speed, $N$, $B$, and $A$

See Alternating Current Generators.

Eddy Currents

When bulk conductors experience changing flux, circular currents are induced inside the material.

Effects

Heating Loss

Energy is dissipated as thermal energy.

Magnetic Braking

Opposing forces slow motion.

Damping

Used in moving-coil instruments.

Reduction

Use laminated cores or slotted metal sheets to reduce current loops.

Transformers Preview

Transformers use electromagnetic induction to change AC voltage levels.

• a primary coil is supplied with AC
• changing magnetic flux occurs in the iron core
• emf is induced in the secondary coil

See:

• Transformers
• Alternating Current

Graph Skills

Flux-Time Graph

From Faraday’s law:

$$\mathcal{E}=-\frac{d(N\Phi )}{dt}$$

So:

• the gradient of a flux-linkage-time graph gives emf
• a steeper slope means larger emf
• zero slope means zero emf

Sinusoidal Relations

For rotating coils:

• flux linkage varies sinusoidally
• induced emf also varies sinusoidally
• emf is phase-shifted relative to flux linkage

Worked Examples

Example 1: Coil Rotated by $90^{\circ }$

A coil initially has maximum flux linkage $NBA$. It is rotated so the final flux linkage is zero in time $\Delta t$.

$$|\mathcal{E}|=\frac{NBA}{\Delta t}$$

Example 2: Magnet Held Still Near Coil

A magnet is stationary near a coil.

Change in flux linkage:

$$0$$

Therefore:

$$\mathcal{E}=0$$

Example 3: Field Doubled in the Same Time Interval

Doubling the change in $B$ doubles the change in flux linkage, so the induced emf doubles.

Formula Sheet

Magnetic Flux

$$\Phi =BA\cos \theta$$

Flux Linkage

$$N\Phi$$

Faraday’s Law

$$\mathcal{E}=-\frac{d(N\Phi )}{dt}$$

Average Form

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

Motional emf

$$\mathcal{E}=Blv$$

Common Pitfalls

• using angle to plane instead of angle to normal
• thinking presence of field causes induction
• forgetting flux linkage includes $N$
• thinking maximum flux means maximum emf
• ignoring the sign meaning in Faraday’s law

See Electromagnetic Induction Common Exam Traps.

Links

• Motional emf
• Electromagnetic Induction Common Exam Traps
• Current Electricity Fundamentals
• Magnetic Fields
• Magnetic Force
• Alternating Current Generators
• Transformers
• Alternating Current
• Electric Fields
• Vectors