Faraday's & Lenz's Laws (AQA A Level Physics): Revision Note

Faraday's & Lenz's laws

• Faraday's law relates the rate of change of flux linkage to the e.m.f. induced in a conductor

• It is defined as:

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

• Lenz’s Law describes 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 that oppose the change causing it

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

Calculating induced EMF

• Faraday's law of induction can be written mathematically as:

$\epsilon =N\frac{∆\Phi }{∆t}$

• Where:

  • $\epsilon$ = induced e.m.f (V)

  • $N$ = number of turns of coil

  • $∆\Phi$ = change in magnetic flux (Wb)

  • $∆t$ = time interval (s)

• This equation shows that the gradient of a magnetic flux linkage against time graph is the e.m.f

• Lenz’s law combined with Faraday’s law is given by the equation:

$\epsilon =-N\frac{∆\Phi }{∆t}$

• 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 (shown by the minus sign)

• 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