Skip to content

The motor effect

Electricity and magnetism · level 7, lesson 2 of 6

A question to start

Hang a loose wire between the poles of a strong magnet and switch on a current. The wire jumps sideways. Which way, and how hard?

The idea

A wire carrying a current in a magnetic field feels a force. For a straight wire of length \(L\) at right angles to the field:

\[F = BIL.\]

If the wire is at an angle \(\theta\) to the field, \(F = BIL\sin\theta\). Along the field, there is no force at all.

The force is at right angles to both the current and the field. Fleming's left-hand rule gives the direction: hold your thumb, first finger and second finger at right angles.

  • First finger: Field (north to south).
  • Second finger: current.
  • Thumb: motion, the force.
NS field B: N to Scurrent into the pageforce

Worked examples

1. A force. 0.5 m of wire carries 3 A at right angles to a 0.2 T field: \(F = 0.2 \times 3 \times 0.5 = 0.3\) N.

2. At an angle. The same wire at 30° to the field: \(F = 0.3 \times \sin 30° = 0.15\) N.

3. The direction. In the diagram, the field points right and the current goes into the page. The left-hand rule gives a force downwards.

Try it

  1. Find the force on 0.2 m of wire carrying 5 A at right angles to a 0.4 T field.
  2. What is the force when the wire lies along the field?
  3. Reverse the current in the diagram. Which way is the force?
  4. A 0.1 m wire in a 0.25 T field feels 0.05 N. Find the current.
Answers
  1. \(0.4 \times 5 \times 0.2 = 0.4\) N.
  2. Zero.
  3. Upwards.
  4. \(I = F/(BL) = 0.05/0.025 = 2\) A.

Common mistake

Using the right hand. Fleming's rule for the motor effect uses the left hand. (The right hand is for generators.)

Where it leads