Magnetic field due to a current in a wire

A wire that moves a compass

In 1820, a Danish scientist, Hans Christian Oersted, was giving a lecture. He noticed that a compass needle close to a wire moved when the current in the wire was switched on. When he switched the current off, the needle came back. So an electric current has a magnetic field. Electricity and magnetism are connected.

The field of a straight wire

Pass a straight wire through a sheet of card, and sprinkle iron filings on the card. Switch on a large current. The filings form circles around the wire. A compass placed on the card shows the direction of the field.

• The field lines are concentric circles around the wire, in a plane at right angles to the wire.
• The lines are closer near the wire, so the field is stronger near the wire, and it becomes weaker farther away.
• When the current is larger, the field is stronger.
• When the current is reversed, the direction of the field is reversed.

The right-hand thumb rule

How do we find the direction of the field? We use the right-hand thumb rule.

Imagine that you hold the wire in your right hand, with your thumb along the direction of the current. Then the fingers curl around the wire in the direction of the magnetic field.

If the current comes out of the page, towards you, the field goes anticlockwise. If the current goes into the page, the field goes clockwise.

You should find that the field halves when the distance doubles, doubles when the current doubles, and turns round when the current is reversed.

How strong is the field?

For a long straight wire, the strength of the field at a distance $r$ is

Here $B$ is the magnetic field in tesla (T), $I$ is the current in ampere, and $r$ is the distance in metre. The constant $\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}$. You need this formula only to see how the field changes: it is proportional to $I$ and inversely proportional to $r$.

For $I = 6\ \text{A}$ at $r = 2.5\ \text{cm} = 0.025\ \text{m}$:

This is about the same as the field of the Earth, so a compass near such a wire is confused.

The field of a circular loop

When we bend a wire into a circle, the field lines near each part of the wire are circles. They get bigger as we go away from the wire. At the centre of the loop, the lines are almost straight lines at right angles to the plane of the loop.

All the parts of the loop make a field in the same direction at the centre. So the fields add up. If we take a coil of $N$ turns close together, the field at the centre is $N$ times as strong as the field of one turn.

Practise with new numbers

Try it in Python

The program finds the field of a straight wire at five distances.

Remember these

• A current has a magnetic field (Oersted). The field lines of a straight wire are circles around it.
• Right-hand thumb rule: thumb along the current, fingers show the field.
• The field is stronger for a larger current and nearer to the wire. A coil of $N$ turns gives $N$ times the field of one turn.

Check yourself

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

1. A straight wire carries a current out of the page. Does its field go clockwise or anticlockwise?

2. What happens to the field of a wire when you move four times as far from it?

3. Why is the field at the centre of a coil of $50$ turns stronger than the field of one loop?

4. Who first showed that a current has a magnetic field, and what did he see?