Force on a current-carrying conductor

A rod that jumps

Hang a short aluminium rod from two thin wires, so that it lies across the gap between the poles of a strong horseshoe magnet. Join the rod to a battery and a switch. When you close the switch, a current flows in the rod, and the rod jumps sideways. A magnet pushes on a wire that carries a current.

We saw in the last lesson that a current makes a magnetic field. Now we see the other side of the same idea: a magnetic field pushes on a current.

What decides the force?

When we try the experiment in different ways, we find these facts:

• The direction of the force changes when the current is reversed.
• The direction of the force changes when the direction of the field is reversed (the poles are changed).
• The force is zero when the wire is parallel to the field, and it is the largest when the wire is at right angles to the field.
• The force is larger for a larger current, and for a stronger field.
• The force is at right angles to both the field and the current.

In the picture, the field goes into the page, and the current goes to the right. The force is up. When the current goes to the left, the force is down.

You should find that the push doubles when the current, the field or the length doubles, and that it turns round when the current does.

Fleming's left-hand rule

The direction of the force is found with Fleming's left-hand rule.

Stretch the forefinger, the middle finger and the thumb of your left hand, so that they are at right angles to one another.

- The forefinger points in the direction of the magnetic field (north to south).

- The middle finger points in the direction of the current.

- Then the thumb shows the direction of the force (the motion) on the conductor.

A short way to remember: Forefinger is Field, the mIddle finger is I, the current, and the thuMb is Motion.

The size of the force

When the wire is at right angles to the field, the force is

where $B$ is the magnetic field in tesla (T), $I$ is the current in ampere, and $L$ is the length of the wire in the field, in metre. For a wire at an angle $\theta$ to the field, $F = BIL\sin\theta$. You need these formulas only to see how the force depends on the quantities.

A worked example

A wire of length $0.1\ \text{m}$ carries a current of $5\ \text{A}$ at right angles to a magnetic field of $0.2\ \text{T}$. What is the force on the wire?

Step 1. We use $F = BIL = 0.2\ \text{T} \times 5\ \text{A} \times 0.1\ \text{m} = 0.1\ \text{N}$.

Step 2. If the wire is turned to make an angle of $30^\circ$ with the field, $F = BIL\sin 30^\circ = 0.1\ \text{N} \times 0.5 = 0.05\ \text{N}$.

Practise with new numbers

Try it in Python

The program finds the force on the wire for four angles between the wire and the field.

Remember these

• A conductor with a current in a magnetic field feels a force.
• The force is largest when the current is at right angles to the field, and it is zero when the current is parallel to the field.
• Fleming's left-hand rule: forefinger = field, middle finger = current, thumb = force.
• $F = BIL$ for a wire at right angles to the field.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A wire carries a current to the left in a field that points into the page. Which way is the force on it?

2. A wire is slowly turned from right angles to the field until it lies along the field. What happens to the force on it?

3. What is the force on a wire of $0.2\ \text{m}$ that carries $4\ \text{A}$ at right angles to a field of $0.5\ \text{T}$?

4. Name two ways to reverse the force on a wire in a magnetic field.