Faraday & Lenz's Law (Edexcel International A Level Physics)

Faraday and Lenz's Law

Faraday's Law

• Faraday's Law connects the rate of change of flux linkage with induced e.m.f

• It is defined in words as:

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

• Faraday's Law as an equation is defined as:

• Where:

  • ε = induced e.m.f (V)

  • Δ(Nɸ) = change in flux linkage (Wb turns)

  • Δt = time interval (s)

• If the interval of time becomes very small (i.e., in the limit of Δt → 0) the equation for Faraday's Law can be written as:

Lenz's Law

• Lenz’s Law is used to predict the direction of an induced e.m.f in a coil or wire

• Lenz's Law is summarised below:

  The induced e.m.f is set up in a direction to produce effects that oppose the change causing it

• Lenz's Law can be experimentally verified using:

  • A bar magnet

  • A coil of wire

  • A sensitive ammeter

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

• A known pole (either north or south) of a bar magnet is pushed into the coil

  • This induces an e.m.f in the coil

  • The induced e.m.f drives a current (because it is a complete circuit)

• Lenz's Law dictates: 

  • The direction of the e.m.f, and hence the current, must be set up to oppose the incoming magnet

  • Since a north pole approaches the coil face, the e.m.f must be set up to create an induced north pole

  • This is because two north poles will repel each other

• The direction of the current is therefore as shown in the image above

  • The direction of current can be verified using the right hand grip rule

  • Fingers curl around the coil in the direction of current and the thumb points along the direction of the flux lines, from north to south 

  • Therefore, the current flows in an anti-clockwise direction in the image shown, in order to induce a north pole opposing the incoming magnet

Combining Lenz's Law and Faraday's Law

• Combining Lenz's Law into the equation for Faraday's Law is written as: 

• The negative sign represents Lenz's Law

  • This is because it shows the induced e.m.f ε is set up in an 'opposite direction' to oppose the changing flux linkage

• This equation also shows that the gradient of the graph of magnetic flux (linkage) against time,  represents the magnitude of the induced e.m.f

  • Note: the negative sign means if the gradient is positive, the induced e.m.f is negative

  • This is again due to Lenz's Law, which says the e.m.f is set up to oppose the effects of the changing flux linkage