Find the force on a current-carrying wire

A wire carrying current in a magnetic field feels a force. The force is at right angles to both the field and the current, and its direction comes from Fleming’s left-hand rule. A stronger field, a larger current or a longer wire in the field all increase the force.

This skill appears in magnetism and fields and underlies the electric motor, so it comes up in both direction and “what changes” questions.

Why does a current feel a force at all?

A current makes its own circular field around the wire (see sketching field patterns). That field interacts with the field of the magnet. On one side of the wire the two fields add and on the other they partly cancel, so the wire is pushed towards the weaker side.

For IGCSE you only need the result, not the field-adding picture: the direction is found by the hand rule, and the size changes in predictable ways.

How do I use Fleming’s left-hand rule?

1. Use the left hand. Hold thumb, first finger and second finger at right angles to each other.
2. First finger: field. Point it along the field, from north to south.
3. Second finger: current. Point it along the conventional current, positive to negative.
4. Thumb: force. It now points the way the wire is pushed.

If you turn the hand to fit the field and the current, the thumb always ends up where the force is. Do not try to keep the hand in one fixed position.

What changes the size of the force?

For a wire at right angles to a uniform field, the force gets larger with a stronger field, a larger current and a longer length of wire in the field. If any of these is zero, the force is zero.

Reversing the current or reversing the field turns the force round. Reversing both leaves the direction unchanged.

Worked example

A wire carries a current of 2.0 A at right angles to a uniform field. The force on it is 0.030 N. (Invented data.)

Part (a). What is the force if the current becomes 3.0 A and nothing else changes?

The force is proportional to the current.

0.030 N ÷ 2.0 A = 0.015 N per ampere. At 3.0 A the force is 0.015 × 3.0 = 0.045 N. Check: the current went up by a factor of 1.5, and 0.030 × 1.5 = 0.045.

Part (b). The current stays at 2.0 A but the magnet is swapped for one with half the field strength. What is the force?

Half the field gives half the force: 0.030 ÷ 2 = 0.015 N.

Part (c). The field points right (north on the left), and the current is out of the page. Which way is the force?

First finger right, second finger out of the page.

The thumb points up the page. Check against the earlier example: current into the page with the same field gave a downward force, so out of the page must give the opposite, upwards. The two answers agree.

The mistake to watch for

A common slip is to use the right hand, or to use electron flow.

Mistaken answer: a student uses electron flow for the second finger and gets a force pointing down when the answer should be up.

The direction of the second finger must be conventional current.

The correction is to read the current direction from the battery: positive to negative. Then use the left hand. If your answer contradicts a quick sanity check, such as reversing one thing should reverse the force, recheck the current.

Check yourself

1. A wire in a field has a force of 0.12 N at 4.0 A. What is the force at 1.0 A with nothing else changed?

2. The current and the field are both reversed at the same time. What happens to the direction of the force?

3. A wire lies along the same direction as the field lines. What is the force?

Where this leads next

The magnetic test lesson uses these ideas in interpretation, and later the induction and transformers module runs the idea in reverse. Try the practice set for mixed questions.

Hand rules are easy to know and hard to use reliably. Our teachers can practise them with you in online one-to-one Physics tuition.