Solenoids

A solenoid is a long coil of wire. When a current flows through it, the magnetic fields of all the turns add together, so the field inside is strong and uniform, and the field outside has the same shape as a bar magnet's. Putting an iron core inside makes the field stronger still: an electromagnet is a solenoid with an iron core, and unlike a permanent magnet it can be switched on and off.

What is a solenoid?

Any wire carrying a current has a magnetic field around it. AQA GCSE Physics says the strength of that field depends on the current and on the distance from the wire. The field around a single straight wire is weak, so to get a useful field the wire is wound into a coil of many turns. That coil is a solenoid, and shaping the wire this way increases the strength of the magnetic field the current produces.

The magnetic field of a solenoid

• Inside: the field lines are straight, parallel and evenly spaced, so the field is uniform: the same strength and direction everywhere near the middle.
• Outside: the lines loop round from one end to the other, exactly like the field of a bar magnet. Field lines leave the north end and go round to the south end.
• The field is strongest inside, where the lines are closest together. Outside a long solenoid the field is very weak.

You can see these patterns by placing small compasses around a solenoid, or explore field lines round magnets in the Field Lines Simulator.

Which end is north?

For a straight wire, the right-hand rule says: point your right thumb along the current and your fingers curl the way the field goes round the wire. Applied to every turn of a solenoid, it gives a quick way to find the poles: curl the fingers of your right hand round the solenoid in the direction the current flows round the turns, and your thumb points to the north end. Reverse the current and the poles swap.

How to make a solenoid's field stronger

The iron core is what turns a solenoid into an electromagnet. The iron becomes an induced magnet in the field of the solenoid, adding to it. When the current stops, an induced magnet loses most or all of its magnetism quickly, so the electromagnet can be switched off.

The field strength formula: B = μ₀nI

Beyond GCSE, the magnetic flux density inside a long solenoid is given by:

μ₀ is the permeability of free space, 4π × 10⁻⁷ T m A⁻¹. The formula assumes the solenoid is much longer than it is wide and has no iron core. It shows the GCSE rules in numbers: doubling the current or the turns per metre doubles B, and the length or width of the coil does not appear at all.

Uses of solenoids and electromagnets

• MRI scanners. OpenStax describes fields of about 2 T made over a large-diameter solenoid for magnetic resonance imaging. Such large currents heat ordinary wire, so superconducting wire is used.
• Steering electron beams. Pairs of coils steered the electron beam in old cathode ray tube (CRT) televisions and monitors.
• Electromagnets, anywhere a magnet needs to be switched on and off.

AQA GCSE Physics (not Combined Science) asks you to interpret diagrams of electromagnetic devices like these and explain how they work: follow what happens when the current switches on, the iron is attracted, and something moves.

Worked examples

Example 1: explaining a stronger field

A student has a solenoid with 50 turns and a current of 0.5 A. Give three changes that make its magnetic field stronger.

1. Increase the current, for example to 1.0 A.
2. Wind more turns onto the same length of coil.
3. Put an iron core inside the solenoid.

Example 2: using B = μ₀nI

A solenoid 0.40 m long has 800 turns and carries a current of 2.5 A. Find the magnetic flux density inside it.

1. Turns per metre: n = 800 ÷ 0.40 = 2,000 m⁻¹.
2. B = μ₀nI = 4π × 10⁻⁷ × 2,000 × 2.5 = 6.28 × 10⁻³ T, about 6.3 mT.
3. If the current is doubled to 5.0 A, B doubles to 12.6 mT.

Common mistakes

• Drawing curved lines inside the solenoid. Inside, the lines are straight, parallel and evenly spaced.
• Arrows going the wrong way. Outside, field lines go from north to south; inside, they continue from south to north, making closed loops.
• Saying any metal core works. It must be a magnetic material, such as iron.
• Calling a solenoid a permanent magnet. It only has a field while current flows.
• Using total turns as n. In B = μ₀nI, n is turns per metre: divide the number of turns by the length.

Practise with a short timed paper

Electromagnetism is in AQA GCSE Physics and Combined Science. The daily GCSE Physics Higher and GCSE Combined Science Higher papers are short timed papers of 8 questions, with a new one every day. For the force on a wire in a field, see Fleming's left-hand rule.

Read next

Physics · Fields and gravityMagnetic field simulation: bar magnets and field linesFree magnetic and electric field simulation: drag bar magnets and charges, watch field lines trace live, and probe the field strength anywhere.