The big idea: A magnetic field is the region around a magnet — or around a current — where a magnetic force is felt.
We picture it with field lines. An electric current makes its own magnetic field, which is why two current-carrying wires can push or pull on each other.
A field line shows the direction the field points; lines closer together mean a stronger field.
[Diagram: phys-field-lines] - Available in full study mode
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.
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
[Diagram: phys-free-body] - Available in full study mode
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.
Worked example — force per unit length
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.)
Solution
- Start with the given formula:
- Put in the numbers (I1 = 3.0, I2 = 4.0, r = 0.10):
- Work it out — keep the unit:
- The currents are in the same direction, so the wires attract.
Final answer
F/L = 2.4 × 10⁻⁵ N m⁻¹, and the wires attract (parallel currents in the same direction).
Feeling unprepared for exams?
Get a clear study plan, practice with real questions, and know exactly where you stand before exam day. No more guessing.
How this is tested: Parallel currents usually appear as a Paper 1A 'scaling' multiple-choice question.
- Paper 1A: you are given a force per unit length, then one current is doubled / halved and/or the separation is changed, and you 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.
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.
[Diagram: phys-free-body] - Available in full study mode
IB-style question — (a) the new force per unit length
Two parallel wires repel each other with a force per unit length of 6.0 × 10⁻⁵ N m⁻¹. The current in one wire is then doubled, and the separation between the wires is also doubled. Find the new force per unit length.
Solution
- Start with the given formula to see what F/L depends on:
- So F/L ∝ I1 I2 / r. Apply each change as a factor: one current × 2, separation × 2 (÷ 2 on the force):
- The factor 2 ÷ 2 = 1, so the force is unchanged:
Final answer
F/L = 6.0 × 10⁻⁵ N m⁻¹ — doubling one current (× 2) and doubling the separation (÷ 2) cancel out.
IB-style question — (b) the direction
The two wires above were repelling, so their currents flow in opposite directions. The current in one wire is now reversed. State whether the wires now attract or repel.
Solution
- Parallel currents in the same direction attract; in opposite directions they repel.
- The wires were repelling, so the currents were opposite. Reversing one current makes both currents point the same way.
- Same-direction currents attract.
Final answer
They now attract — reversing one current makes the two currents parallel (same direction), which attract.