Faraday's & Lenz's Laws

Faraday’s law tells us the magnitude of the induced e.m.f in electromagnetic induction and is defined as:

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

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

$ε = N \frac{∆ Φ}{∆ t}$

Where:
- ε = induced e.m.f (V)
- N = number of turns of coil
- ΔΦ = change in magnetic flux (Wb)
- Δt = time interval (s)
Lenz’s Law gives the direction of the induced e.m.f as defined by Faraday’s law:

The induced e.m.f acts in such a direction to produce effects which oppose the change causing it

Lenz’s law combined with Faraday’s law is:

$ε = - N \frac{∆ Φ}{∆ t}$

This equation shows:
- When a bar magnet goes through a coil, an e.m.f is induced within the coil due to a change in magnetic flux
- A current is also induced which means the coil now has its own magnetic field
- The coil’s magnetic field acts in the opposite direction to the magnetic field of the bar magnet

If a direct current (d.c) power supply is replaced with an alternating current (a.c) supply, the e.m.f induced will also be alternating with the same frequency as the supply

Experimental evidence for Lenz’s law

To verify Lenz’s law, the only apparatus needed is:
- a bar magnet
- a coil of wire
- a sensitive ammeter

Note: a cell is not required
A known pole (either north or south) of the bar magnet is pushed into the coil, which induces a magnetic field in the coil
- Using the right hand grip rule, the curled fingers indicate the direction of the current and the thumb indicates the direction of the induced magnetic field

The direction of the current is observed on the ammeter
- Reversing the magnet direction would give an opposite deflection on the meter

The induced field (in the coil) repels the bar magnet
This is because of Lenz’s law:
- The direction of the induced field in the coil pushes against the change creating it, i.e. the bar magnet

Lenz's law

20-2-lenzs-law-experiment-1

Lenz’s law can be verified using a coil connected in series with a sensitive ammeter and a bar magnet

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.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° in a time 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
Time interval, Δt = 0.18 s
Angle between coil and field lines, θ = 40^o

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

$ε = N \frac{∆ Φ}{∆ t}$

Step 3: Write out the equation for flux linkage

$N Φ = B A N \cos (θ)$

Step 4: Substitute values into flux linkage equation:

$N Φ = (80 \times 10^{- 3}) \times (4.9 \times 10^{- 4}) \times 350 \times \cos (40) = 0.0105 Wb turns$

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

$ε = \frac{0.0105}{0.18} = 0.05839 = 58 mV (2 s . f .)$

Faraday's & Lenz's Laws (CIE A Level Physics)

Revision Note