Solenoids and electromagnets

A magnet that you can switch off

A crane in a scrapyard lifts a car with a huge magnet, and then drops it when the operator switches the magnet off. This magnet is not a permanent magnet. It is made with a current. To see how, let us study a coil.

The solenoid

A solenoid is a long coil of many circular turns of insulated wire, wound close together in the shape of a cylinder.

When a current flows in a solenoid, the fields of all the turns add up.

• Inside the solenoid, the field lines are straight and parallel, and close together. The field is strong and the same at every point, which we call a uniform field.
• Outside, the field lines curve around from one end to the other, like the lines of a bar magnet.
• One end of the solenoid behaves like a north pole and the other like a south pole. We can find which is which with the right-hand thumb rule: curl the fingers of the right hand along the current in the turns, and the thumb points to the north pole.

So a solenoid that carries a current is a bar magnet that we can switch on and off.

How strong is it?

For a long solenoid with $n$ turns in each metre, the field inside is

with $\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}$. The field is stronger when

• the current $I$ is larger,
• the number of turns in each metre $n$ is larger.

You should find that doubling the current, or the turns in each metre, doubles the field inside.

The electromagnet

If we put a piece of soft iron inside the solenoid, the field becomes hundreds of times stronger, because the iron itself becomes a magnet while the current flows. The solenoid with the iron core is an electromagnet.

• The core must be soft iron. Soft iron is magnetised quickly and loses its magnetism almost at once when the current is switched off. Steel would stay magnetised.
• The strength of the electromagnet can be changed with the current, with the number of turns, and with the core.

Uses of electromagnets

• Cranes in scrapyards, to lift and drop iron and steel.
• Electric bells. The electromagnet pulls a hammer to the gong, and the circuit breaks, so the hammer springs back. Then the circuit is made again, and this repeats.
• Relays, in which a small current in an electromagnet switches a large current on and off.
• Loudspeakers, motors and generators.
• Hospitals, to take out small pieces of iron from the eye, and in the large machine for magnetic resonance imaging (MRI).

A worked example

A solenoid has $400$ turns in a length of $0.2\ \text{m}$, and it carries a current of $2.5\ \text{A}$. What is the field inside?

Step 1. The number of turns in each metre is $n = \dfrac{400}{0.2\ \text{m}} = 2000$ turns per metre.

Step 2. $B = \mu_0\,n\,I = 4\pi \times 10^{-7}\ \text{T m/A} \times 2000\ \text{m}^{-1} \times 2.5\ \text{A} = 6.3 \times 10^{-3}\ \text{T}$.

So the field is about $6.3\ \text{mT}$. This is about $125$ times the field of the Earth.

Practise with new numbers

Try it in Python

The program finds the field inside a solenoid of $1000$ turns in each metre for four currents.

Remember these

• A solenoid is a long coil. Its field is like that of a bar magnet, and it is uniform inside.
• A soft iron core inside it makes an electromagnet, which is strong and can be switched on and off.
• The field grows with the current and with the number of turns in each metre.

Check yourself

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

1. What would go wrong if the core of a scrapyard crane's electromagnet were made of steel?

2. Name three ways to make an electromagnet stronger.

3. What happens to the poles of an electromagnet when the current is reversed?

4. A solenoid has $800$ turns in $0.4\ \text{m}$ and carries $2\ \text{A}$. What is the field inside? Take $\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}$.