Faraday's Law of Electromagnetic Induction

Michael Faraday discovered in 1831 that a changing magnetic flux through a circuit induces an electromotive force (EMF). This is the foundation of electromagnetic induction. The magnitude of the induced EMF is proportional to the rate of change of magnetic flux linkage through the circuit.

Faraday's Law

EMF = -N × (ΔΦ / Δt)

EMF

Electromotive force (volts, V)

N

Number of turns in the coil

ΔΦ

Change in magnetic flux (Wb)

Δt

Change in time (seconds, s)

Magnetic flux (Φ): Φ = B × A × cosθ, where B is the magnetic field strength (T), A is the area of the loop (m²), and θ is the angle between B and the normal to the surface.

Key insight: The negative sign in Faraday's law represents Lenz's law -- the induced EMF always opposes the change in flux that produced it.

Lenz's Law

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that caused it. This is a consequence of the conservation of energy -- if the induced current aided the change, it would create a perpetual motion machine, violating this fundamental law.

Magnet Moving into a Coil

N

↓

Coil

North pole approaching

Induced current opposes → repels magnet

|

Coil

↓

N

North pole moving away

Induced current opposes → attracts magnet

Practical use of Lenz's law: Electromagnetic braking in trains uses Lenz's law. Eddy currents induced in the rail or disc oppose the motion, slowing the vehicle without physical contact.

Generators and Transformers

Electromagnetic induction is the operating principle behind electric generators (which convert mechanical energy to electrical energy) and transformers (which change the voltage of alternating current).

AC Generator

A coil rotates in a magnetic field, causing the magnetic flux through the coil to change continuously.

This produces a sinusoidal alternating EMF:

EMF = NBAω sin(ωt)

where ω is the angular frequency of rotation

Peak EMF occurs when the coil is parallel to the field (maximum rate of flux change).

Transformer

Two coils (primary and secondary) wound around a shared iron core. AC in the primary creates a changing flux that induces an EMF in the secondary.

V_p/V_s = N_p/N_s

Step-up: N_s > N_p (increases voltage)

Step-down: N_s < N_p (decreases voltage)

For an ideal transformer: V_pI_p = V_sI_s

How a Transformer Works

AC Input

Alternating current

→

Primary Coil

N_p turns

→

Iron Core

Channels magnetic flux

→

Secondary Coil

N_s turns

→

AC Output

Transformed voltage

Key Vocabulary

Magnetic Flux (Φ)

A measure of the total magnetic field passing through a given area; Φ = BA cosθ, measured in webers (Wb).

Electromotive Force (EMF)

The potential difference produced by electromagnetic induction or a battery, measured in volts (V). It drives current through a circuit.

Eddy Currents

Loops of electric current induced within conductors by a changing magnetic field. They cause energy loss as heat in transformer cores.

Turns Ratio

The ratio of the number of turns in the primary coil to the secondary coil of a transformer (N_p/N_s), which determines the voltage transformation.

Worked Examples

1

A coil of 200 turns has a magnetic flux that changes from 0.05 Wb to 0.02 Wb in 0.1 s. Calculate the induced EMF.

Step 1: Identify the values: N = 200, ΔΦ = 0.02 - 0.05 = -0.03 Wb, Δt = 0.1 s.

Step 2: Apply Faraday's law: EMF = -N × (ΔΦ / Δt).

Step 3: EMF = -200 × (-0.03 / 0.1) = -200 × (-0.3) = 60 V.

Answer: The induced EMF is 60 V.

2

A step-up transformer has 500 turns on the primary and 2000 turns on the secondary. If the input voltage is 240 V, what is the output voltage?

Step 1: Use the transformer equation: V_p/V_s = N_p/N_s.

Step 2: Rearrange: V_s = V_p × (N_s/N_p) = 240 × (2000/500).

Step 3: V_s = 240 × 4 = 960 V.

Answer: The output voltage is 960 V.

3

A magnet is pushed into a solenoid. Use Lenz's law to explain what happens.

Step 1: As the magnet enters the solenoid, the magnetic flux through the coil increases.

Step 2: By Lenz's law, the induced current must create a magnetic field that opposes the increase in flux.

Step 3: The solenoid's induced field will have the same polarity facing the magnet (e.g., if the north pole approaches, the near end of the solenoid becomes a north pole).

Answer: The induced current creates a field that repels the approaching magnet, opposing the change in flux. Energy must be supplied to push the magnet in, consistent with conservation of energy.

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

According to Faraday's law, the magnitude of the induced EMF is proportional to:

The rate of change of magnetic flux through the coil The total magnetic flux through the coil The strength of the magnetic field only The area of the coil only

Question 2

Lenz's law is a consequence of which fundamental principle?

Conservation of charge Conservation of energy Conservation of momentum Conservation of mass

Question 3

A transformer has 100 primary turns and 400 secondary turns. If the primary voltage is 12 V, the secondary voltage is:

3 V 12 V 48 V 4800 V

Question 4

In an AC generator, the EMF is maximum when the coil is:

Perpendicular to the magnetic field Stationary in the magnetic field At 45 degrees to the magnetic field Parallel to the magnetic field

Question 5

A coil of 50 turns experiences a flux change of 0.4 Wb in 0.2 s. The induced EMF is:

100 V 40 V 10 V 4 V

Electromagnetic Induction