Magnets and the Magnetic Field of a Current: Quick Revision

A brief note on Magnets and the Magnetic Field of a Current. Read it before a test. Try each question at the end before you open its answer.

The big ideas

• A magnet has a north pole and a south pole. Like poles repel; unlike poles attract.
• Field lines run from north to south outside a magnet and back inside it: closed loops. They crowd together where the field is strong, and never cross.
• A current has a magnetic field (Oersted). Round a straight wire the lines are circles.
• Right-hand thumb rule: thumb along the current, the fingers curl the way the field goes.
• A coil of $N$ turns gives $N$ times the field of one loop. A solenoid has a strong, uniform field inside, like a bar magnet that can be switched off.
• A soft iron core makes an electromagnet: much stronger, and it loses its magnetism when the current stops.

The facts at a glance

• Field of a long wire: rule: $B = \dfrac{\mu_0 I}{2\pi r} = 2 \times 10^{-7}\,\dfrac{I}{r}$; unit: tesla (T)
• Turns in each metre: rule: $n = \dfrac{N}{L}$; unit: per metre
• Field in a solenoid: rule: $B = \mu_0 n I$; unit: tesla (T)
• The constant: rule: $\mu_0 = 4\pi \times 10^{-7}$; unit: T m/A

A worked example

A long wire carries $11\ \text{A}$. Find its field $4\ \text{cm}$ away. Then find the field inside a solenoid of $360$ turns, $0.2\ \text{m}$ long, carrying $0.8\ \text{A}$.

1. The wire. $B = 2 \times 10^{-7}\ \text{T m/A} \times \dfrac{11\ \text{A}}{0.04\ \text{m}} = 5.5 \times 10^{-5}\ \text{T} = 55\ \mu\text{T}$.
2. Turns in each metre. $n = \dfrac{360}{0.2\ \text{m}} = 1800$ turns per metre.
3. The solenoid. $B = 4\pi \times 10^{-7}\ \text{T m/A} \times 1800\ \text{m}^{-1} \times 0.8\ \text{A} = 1.81 \times 10^{-3}\ \text{T} = 1.81\ \text{mT}$.

Practice with new numbers

A program to try

The program works out both fields of the worked example.

Mistakes to avoid

• Leaving the distance in centimetres in $B = 2 \times 10^{-7}\,\dfrac{I}{r}$. Use metres.
• Using all the turns as $n$. $n$ is the number of turns in each metre.
• Saying field lines start and stop at the poles. They are closed loops.
• Using steel for an electromagnet. Steel stays magnetised.

Check yourself

1. A wire on the page carries a current up the page. Just to the right of the wire, does its field point into the page or out of it?

2. A wire's field is $60\ \mu\text{T}$ at $2\ \text{cm}$. What is it at $8\ \text{cm}$?

3. A solenoid has $1250$ turns in each metre and carries $2\ \text{A}$. What is the field inside? Take $\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}$.

4. Why does a scrapyard crane's electromagnet drop its load when the current is switched off?