Magnetic Fields due to Currents

A current produces a magnetic field. Around a straight wire the field lines are concentric circles (right-hand grip rule), weakening with distance. A flat coil's field resembles a short bar magnet; a long solenoid gives a strong, uniform field inside, which a soft iron core greatly increases. Two parallel wires each sit in the other's field, so they exert forces on each other: currents in the same direction attract, opposite directions repel.

Cambridge 9702 Paper 4Edexcel YPH11 WPH14AQA 7408 Paper 2≈ 30 minRevision 5 · updated 2026-10-27

Section 1 of 14

Learning objectives

Sketch field patterns for a straight wire, a flat coil and a solenoid.
Use the right-hand grip rule to find field directions.
Explain the effect of a ferrous core.
Explain and find the direction of forces between parallel conductors.

Pause and think

Two parallel wires carry currents in the same direction. Is there a force between them, and which way?

Section 2 of 14

Core idea

Start hereDefining the ampere

Two parallel wires carrying currents pull on each other. For decades the ampere was defined by exactly how hard: currents make magnetic fields, and those fields push on other currents.

The big idea

Wire: circular field, $B\propto\frac Ir$ . Solenoid: uniform inside, $B\propto nI$ . Parallel currents attract; antiparallel repel.

1. Field patterns

Field of a solenoid

Inside, the field lines are parallel and evenly spaced: a uniform field. Outside, it looks like a bar magnet's field.

Field strength round a long straight wire falls with distance

Twice as far: half the field. More current: stronger field.

Wire: right-hand grip rule; $B\propto\frac Ir$ .
Solenoid: $B\propto nI$ ( $n$ turns per metre); iron core increases it greatly.

2. Forces between wires

Worked exampleCurrents in the same direction

Two parallel wires.

Goal: Attract or repel?
Strategy: Field of one at the other; then left-hand rule.

Grip rule: wire 1's field at wire 2 points (say) into the page.
Left-hand rule on wire 2: force towards wire 1.
Newton's third law: wire 1 pulled towards wire 2.

AnswerAttraction.

✓ CheckReverse one current and both forces reverse: repulsion ✓.

Worked exampleScaling the field

Field 2.0 mT at 1 cm from a wire. At 4 cm? With double current at 4 cm?

Goal: Two fields.
Strategy: $B\propto I/r$ .

$2.0\times\tfrac14=0.5\text{ mT}$
4× distance.
$0.5\times2=1.0\text{ mT}$
2× current.

Answer

0.5

mT;

1.0

mT.

✓ CheckInverse (not inverse-square) with distance ✓.

Common misconceptionLike currents repel Opposite to charges: like currents attract.

Summary

Grip rule; solenoid uniform inside.
Same direction attract.

Solenoid: Long coil of wire.

HistoryAmpère's week. A week after hearing of Ørsted's discovery in

1820

, André-Marie Ampère showed that two parallel currents attract or repel. He went on to develop the mathematical theory of electrodynamics so quickly that Maxwell later called him "the Newton of electricity".

Fun factScrapyard magnets. The electromagnets that lift cars in scrapyards are huge solenoids with iron cores, giving fields over

1

T. Switch off the current and the soft iron loses most of its magnetism, so the car drops exactly where the operator wants.

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