# Lenz's law

## Summary

Faraday's law gives the magnitude of the EMF induced due to a change in flux. Lenz's law tells us the direction.

## Get the basics

#### Definition

Lenz's law states that the direction of the induced current is such that it will oppose the change producing it. This means that we can now state the equation for the induced EMF:

$$\varepsilon =-{\mathrm{d}N\Phi\over \mathrm{d}t}$$

• $$\varepsilon$$ is the induced EMF (V)
• $$N\Phi$$ is the magnetic flux linkage (Tm2 or Wb)
• $${\mathrm{d}N\Phi\over \mathrm{d}t}$$ is the rate of change of magnetic flux linkage (Tm2s-1 or Wb s-1)

#### Sliding wire

To fully understand the cause of Lenz's law, we must consider the motion and forces exerted by individual charges.

### Conservation of energy

Lenz's law is a consequence of Conservation of energy. An induced EMF does work on charges causing them to move in a net direction (and hence for a current to flow).

The induction of current requires energy. Therefore, either:

• work must be done to continue the relative motion of the magnetic field and conductor
• the conductor or magnet will lose kinetic energy so that the EMF induced decreases

## Stretch for 7

### Induced EMF direction

Lenz's law has implications for any instance of electromagnetic induction. There are two mechanisms for determining the direction of the EMF:

1. Consider the direction in which individual moving charges experience a force. This is directed by Fleming's left hand rule.

1. Consider the direction in which EMF is induced by a conductor moving relative to a magnetic field. The switch to the right hand rule incorporates the opposing nature set by Lenz's law.

It can sometimes be difficult for learners to work out the EMF direction because of uncertainty in whether to consider individual charges or the whole of the conductor.

The good news is that there is a simple solution: since we know the consequence of Lenz's law is to oppose the change producing it, the resulting electromagnet formed will always:

• repel an incoming magnetic field
• attract an outgoing magnetic field

#### Falling magnet

When a magnet falls through a conductor, the current direction in the conductor is such as to exert an upward force on the magnet.

#### Coil and magnet

When a magnet moves towards a coil, the current direction in the coil is such as to repel the approaching magnet.

If a north pole moves to the right towards a coil, the coil will become an electromagnet with a north pole on its left.

The right hand grip rule can be used to verify that the direction of conventional current would do so. Note that the current in the side of the coil nearest the reader is upward.

#### Coil in a changing field

When a coil is placed next to an electromagnet coil, the field produced by the induction in the second coil will be in the opposite direction to the field produced by the first coil.

### Eddy currents

Eddy currents are induced within a conductor. They flow in closed loops that is perpendicular to the magnetic field. These currents themselves cause the conductor to become an electromagnet.

Eddy currents cause dissipation of thermal energy in devices that employ electromagnetic induction. This can be useful in braking but wasteful in generators and transformers. One mechanism to reduce eddy currents is to laminate any soft iron core present.

## Test yourself

Use quizzes to practise application of theory.