Faraday’s Law of Induction (HL) | HL IB Physics Revision Notes 2025

Faraday’s Law of Induction

Faraday's Law connects the rate of change of magnetic flux linkage with induced e.m.f
It is defined in words as:

The magnitude of an induced e.m.f is directly proportional to the rate of change of magnetic flux linkage

Faraday's Law of induction is defined by the equation:

$ε = \frac{N (∆ Φ)}{∆ t}$

Where:
- $ε$ = induced e.m.f (V)
- $N ∆ (Φ)$ = change in magnetic flux linkage (Wb turns)
- $∆ t$ = time interval (s)

When a coil is completely vertical relative to the magnetic field lines:
- The change in magnetic flux linkage is at a maximum - the field lines are travelling through the area of the coil
- There is no e.m.f induced - there is no cutting of field lines i.e. there is no change in magnetic flux linkage

When a coil is completely horizontal relative to the magnetic field lines:
- The change in magnetic flux linkage is zero - there are no field lines travelling through the area of the coil
- Maximum e.m.f is induced - there is the maximum cutting of field lines

Coil Turning E.m.f

Emf induced and the rotation of a coil

Worked example

A small rectangular coil contains 350 turns of wire. The longer sides are 3.5 cm and the shorter sides are 1.4 cm.

4-4-2-faradays-law-worked-example

The coil is held between the poles of a large magnet so that the coil can rotate about an axis through its centre. The magnet produces a uniform magnetic field of flux density 80 mT between its poles.

The coil is positioned horizontally and then turned through an angle of 40° over a time interval of 0.18 s.

Calculate the magnitude of the average e.m.f induced in the coil.

Answer:

Step 1: Write down the known quantities

Magnetic flux density, B = 80 mT = 80 × 10^-3 T
Area, A = 3.5 × 1.4 = (3.5 × 10^-2) × (1.4 × 10^-2) = 4.9 × 10^-4 m²
Number of turns, N = 350
Angle of rotation, θ = 40°
Time interval, Δt = 0.18 s

Step 2: Write down the equation for Faraday’s law:

$ε = \frac{N (∆ Φ)}{∆ t}$

Step 3: Write out the equation for the change in flux linkage:

The number of turns N and the coil area A stay constant
The flux through the coil changes as B cos θ as it rotates
Therefore, the equation to use is:

$N (∆ Φ) = N B A \cos θ$

Step 4: Determine the change in magnetic flux linkage

The initial flux through the coil is zero (flux lines are parallel to the coil face)
The final flux through the coil is 80 mT (flux lines are more perpendicular to the coil face)
This is because the coil begins horizontally in the field and is rotated by 40°
Therefore, the change in flux linkage is:

$N ∆ (Φ) = N B A \cos θ = 350 \times (4.9 \times 10^{- 4}) \times (80 \times 10^{- 3}) \times \cos 40$

$N (∆ Φ)$ = 0.011 Wb turns

Step 5: Substitute the change in flux linkage and time into Faraday’s law equation:

$ε = \frac{0.011}{0.18} = 0.061 V$

Exam Tip

The important point to notice is that an emf is induced in a conductor in a magnetic field if there is change in flux linkage. This means, the conductor (e.g. a coil) must cut through the field lines to have an emf (and hence a current) induced.

Faraday’s Law of Induction (HL) (HL IB Physics)

Revision Note