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Electromagnets

Electricity and magnetism · level 7, lesson 1 of 6

A question to start

A scrapyard crane lifts a whole car with a magnet, then drops it at the flick of a switch. How can a magnet be switched off?

The idea

Every current makes a magnetic field around it. Around a long straight wire, the field lines are circles, and the field at a distance \(r\) is

\[B = \frac{\mu_0 I}{2\pi r}, \qquad \mu_0 = 4\pi \times 10^{-7} \text{ T m/A}.\]

Grip the wire with your right hand, thumb along the current: your fingers curl the way the field goes.

Wind the wire into a long coil, a solenoid, and the fields add up inside it into a strong, even field:

\[B = \mu_0 n I,\]

where \(n\) is the number of turns per metre. Put an iron core inside and the field becomes hundreds or thousands of times stronger. Switch off the current, and the field goes.

field circles a wirecoil with an iron corecurrent in the turns

Worked examples

1. A wire. 10 A, 1 cm away: \(B = 4\pi\times10^{-7} \times 10/(2\pi \times 0.01) = 2\times10^{-4}\) T, 200 µT, about four times Earth's field.

2. A solenoid. 1,000 turns per metre, 2 A: \(B = 4\pi\times10^{-7} \times 1000 \times 2 = 2.5\times10^{-3}\) T, 2.5 mT.

3. An iron core. Suppose iron makes the field 1,000 times stronger: 2.5 T, enough to lift steel.

Try it

  1. Find the field 5 cm from a wire carrying 20 A.
  2. A solenoid has 500 turns in 0.25 m and carries 3 A. Find the field inside.
  3. Name two ways to make an electromagnet stronger.
  4. Why is an electromagnet better than a permanent magnet for a scrapyard crane?
Answers
  1. \(2\times10^{-7} \times 20/0.05 = 8\times10^{-5}\) T, 80 µT.
  2. \(n = 2000\) per m: \(B = 4\pi\times10^{-7} \times 2000 \times 3 = 7.5\times10^{-3}\) T.
  3. Any two: more current, more turns per metre, an iron core.
  4. It can be switched off to drop the load.

Common mistake

Using the total number of turns for \(n\). \(n\) is turns per metre: divide the turns by the coil's length.

Where it leads