Topic Menu

Cyber-chess a chess instruction site

Force on a current-carrying wire in a magnetic field

A wire has millions of randomly moving charges within it.

When no current flows there is no current because the random movement results in no net flow of charge. It means that there are equal numbers of charged particles moving in opposite directions, cancelling out any net charge. This also means that the magnetic effect of the moving charges is also cancelled out and there will be no net magnetic field

Wires carrying current, however, do have a net flow of charge with an average drift velocity of 'v'.

The total net charge flowing in that direction and the velocity v can be ascertained from the length of the wire and the current flowing.

It can be shown that 'qv' can be expressed in terms of 'Il', where I is the current in a wire, and l is the length, in meters, of the wire—both qv and Il can be expressed in units of C m s-1.

We know that a charge experiences a force when it moves in a magnetic field. See here.

Therefore it is logical that a current carrying wire will also experience a force when in a magnetic field.

F = Bqv sinθ

so,

F = BIl sinθ

At GCSE you will have seen a demonstration of this when you studied the motor effect (see here).

There is a 'Flip Book' with questions on this topic - and (of course) worked solutions!