The big idea: Hold a compass next to a wire and switch on the current — the needle swings. The moving charge has wrapped the wire in a magnetic field.
Magnetic fields
- A magnetic field is the region around a magnet, or a current, where a magnetic force is felt.
- We picture it with field lines — lines closer together mean a stronger field.
- Because a current makes its own field, two current-carrying wires can push or pull on each other.
The four field patterns
Around a straight wire
- Field lines are concentric circles centred on the wire
- They get further apart the further from the wire (field gets weaker)
- Right-hand grip rule: thumb along the current I, fingers curl the way the circles point
Between two bar magnets
- Field lines run from the N pole to the S pole (outside the magnet)
- Unlike poles (N–S) facing → lines join up → the magnets attract
- Like poles (N–N or S–S) facing → lines push apart → the magnets repel
Spot it: Around a wire → circles. Between magnets → lines from N to S.
Unlike poles attract; like poles repel. A current carries a magnetic field with it.
Which end is N?: For a solenoid or coil, curl the fingers of your right hand the way the current goes round: your thumb points to the N end.
A compass points along the field: its N end shows the field direction.
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Each wire sits in the magnetic field made by the other, so each feels a force. The rule for the direction is simple:
Parallel currents (same direction)
- Currents point the same way (e.g. both up the page)
- The wires ATTRACT — they are pulled toward each other
- Memory aid: 'friendly' currents (same way) come together
Anti-parallel currents (opposite directions)
- Currents point opposite ways (one up, one down the page)
- The wires REPEL — they are pushed apart
- Memory aid: 'opposite' currents push off
Parallel currents attract: wire 1 (off to the left) pulls wire 2 toward it. By Newton's third law wire 1 feels an equal force pulling it toward wire 2 — the same force per unit length on each.
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For the size of the force, the data booklet gives the force per unit length (the force on each metre of wire):
- force per unit length on each wire (N m⁻¹)
- permeability of free space (4π × 10⁻⁷ T m A⁻¹)
- current in the first wire (A)
- current in the second wire (A)
- separation between the two wires (m)
How it scales: F/L is proportional to each current and inversely proportional to the separation r.
So doubling one current doubles F/L; doubling the separation halves it.
Two long parallel wires are 0.10 m apart. They carry currents of 3.0 A and 4.0 A in the same direction. Find the force per unit length on each wire, and state whether they attract or repel. (Take μ0 = 4π × 10⁻⁷ T m A⁻¹.)
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How this is tested — parallel currents mostly appear as a scaling question:
Paper 1A
- Given a force per unit length, then one current is doubled/halved and/or the separation changes — find the new F/L and its direction (attract or repel).
Paper 1B / 2
- Describe or draw the field pattern, or use F/L = μ0 I1 I2 / (2π r) directly.
The classic trap: Forgetting that reversing one current flips attract ↔ repel — and that the force changes by a ratio, so you rarely need μ0 at all.
Scale by ratios: F/L ∝ I1 I2 / r. To get the new force, multiply the old one by each change:
× (factor on I1) × (factor on I2) ÷ (factor on r). The constant μ0 ÷ (2π) cancels.
Anti-parallel currents repel: with wire 1 off to the left, wire 2 is pushed to the right, away from wire 1. Each wire feels an equal and opposite push.
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Two parallel wires repel each other with a force per unit length of 6.0 × 10⁻⁵ N m⁻¹. (a) The current in one wire is doubled and the separation is also doubled — find the new force per unit length. (b) Starting from the original repelling wires, the current in one wire is instead reversed — state whether the wires now attract or repel.
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