Quick answer: The magnetic field at the centre of a current-carrying circular coil is stronger when the current is larger, the number of turns is larger and the radius is smaller. Inside a long solenoid the field lines are straight and parallel, so the field is uniform. Its strength increases with current, turns per unit length, and a soft iron core, which turns the solenoid into an electromagnet.
Magnetic field of a circular coil
When a straight current-carrying wire is bent into a circular loop, every part of the wire produces its own magnetic field.
- Near the wire: the field lines are concentric circles around the wire, just as for a straight conductor.
- Towards the centre: these circles become larger and larger.
- At the centre: the field lines are nearly straight and perpendicular to the plane of the loop.
Why straight at the centre? By the right-hand thumb rule, every small part of the loop produces a field that points in the same direction inside the loop. These fields add up, giving a strong field along the axis at the centre.
Factors affecting the field of a circular coil
| Factor | Effect on field at the centre | Relation |
|---|---|---|
| Current (I) | Larger current, stronger field | B ∝ I |
| Number of turns (n) | More turns, stronger field | B ∝ n |
| Radius of coil (r) | Smaller radius, stronger field | B ∝ 1/r |
Why does a coil of n turns give n times the field? The current in every turn flows in the same direction, so the fields of the individual turns add up. A coil of n turns therefore produces a field about n times that of a single turn.
What is a solenoid?
A solenoid is a coil of many circular turns of insulated copper wire wound closely in the shape of a cylinder.
Field pattern of a solenoid
- Like a bar magnet: The field lines around a current-carrying solenoid are similar to those of a bar magnet. One end behaves like a north pole and the other like a south pole.
- Uniform field inside: Inside the solenoid the field lines are straight and parallel. This shows that the magnetic field is the same in strength and direction at all points inside, that is, it is uniform.
- Outside: The lines spread out and curve from one end to the other, as for a bar magnet.
Factors affecting the field of a solenoid
- Current: A larger current produces a stronger field.
- Turns per unit length: A more closely wound solenoid (more turns per metre) produces a stronger field.
- Core material: Placing a rod of soft iron inside the solenoid makes the field very much stronger. This arrangement is called an electromagnet.
Why soft iron?
- Soft iron becomes strongly magnetised when current flows, which greatly increases the field.
- It loses most of its magnetism quickly when the current is switched off, so the electromagnet can be turned on and off.
- Steel keeps its magnetism after the current stops, so it is used to make permanent magnets instead.
Summary table
| Arrangement | Field pattern | Field increases with | Notes |
|---|---|---|---|
| Straight wire | Concentric circles | Larger current; nearer the wire | Direction by right-hand thumb rule |
| Circular coil | Nearly straight at the centre | Larger current, more turns, smaller radius | Field perpendicular to the plane of the coil |
| Solenoid | Uniform inside, like a bar magnet outside | Larger current, more turns per length, soft iron core | Soft iron core makes an electromagnet |
Exam tips
- When drawing a solenoid's field, make the lines inside straight, parallel and evenly spaced, and put arrows on every line.
- Use the right-hand thumb rule to find the direction of the field, and name the rule in your answer.
- For "how can you increase the strength of a solenoid's field?", give three points: more current, more turns, soft iron core.
- For a circular coil, remember the extra factor: a smaller radius gives a stronger field.
Common mistakes
- Saying the field inside a solenoid is zero or circular. It is uniform and in straight lines.
- Forgetting arrows on field lines. Outside the solenoid they go from N to S; inside they go from S to N, so each line is a closed loop.
- Writing that a larger radius gives a stronger field for a circular coil. It is the opposite.
- Suggesting steel for an electromagnet core. Steel stays magnetised; soft iron is used.
Frequently Asked Questions
What factors affect the magnetic field of a circular coil?
The field at the centre increases with the current and the number of turns, and decreases as the radius of the coil increases.
Why is the magnetic field inside a solenoid uniform?
Inside a long solenoid the field lines are straight, parallel and equally spaced, which means the field has the same strength and direction at every point.
How is the field of a solenoid similar to a bar magnet?
The pattern of field lines around a current-carrying solenoid is similar to that around a bar magnet, with one end acting as a north pole and the other as a south pole.
Why is soft iron used as the core of an electromagnet?
Soft iron greatly strengthens the field while current flows and loses most of its magnetism when the current is switched off, so the magnet can be controlled.
Why are the field lines nearly straight at the centre of a circular loop?
Every part of the loop produces a field pointing in the same direction inside the loop. At the centre these fields add up and the lines become nearly straight.