Short on time? This page is the recap. For explanations, figures and the worked examples, use the full study guide.
Recap
- A current makes a magnetic field. Around a long straight wire the field lines are circles centred on the wire; B is tangent to them, with no part towards, away from or along the wire.
- Right-hand rule (field): thumb along the current, fingers curl the way B goes. Current into the page gives clockwise circles.
- Loop: at the centre, B points along the axis. Curl fingers with the current; the thumb gives B.
- Superposition: add the fields of several wires as vectors. They can cancel.
- Right-hand rule (force): fingers along the current, curl towards B, thumb gives F.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| B = μ₀I / (2πr) | μ₀/(2π) = 2 × 10⁻⁷ T·m/A; r in m from the wire’s centre | find the field of a long straight wire |
| B ∝ I, B ∝ 1/r | ratios | predict factors of change |
| F = IℓB sin θ | ℓ = length in the field; θ between current and B | find the force on a wire |
| F/ℓ = μ₀I₁I₂ / (2πd) | d = separation | find the force between parallel wires |
| Situation | Result |
|---|---|
| Wire at right angles to B | F = IℓB (largest) |
| Wire parallel to B | F = 0 |
| Parallel wires, same direction | attract |
| Parallel wires, opposite directions | repel |
Assumptions behind the numbers
- Wires are long and straight compared with the distance r.
- Current is conventional current (the direction positive charge would move).
- The field B in F = IℓB sin θ is uniform over the length ℓ.
Mistakes to avoid
- Radial field lines. That is an electric-field picture.
- Using 1/r². The wire field goes as 1/r.
- Adding magnitudes. Add vectors: opposite fields subtract, perpendicular ones combine by Pythagoras.
- Force along B. The force is at right angles to B.
- Unequal forces between wires. They form a third-law pair.
- Whole length for ℓ. Use only the part in the field.
Quick self-check
- Find B at 2.0 cm from a long wire carrying 3.0 A. (3.0 × 10⁻⁵ T)
- A 0.10 m wire carries 2.0 A at right angles to a 0.50 T field. Find the force. (0.10 N)
- The current is tripled and the distance is tripled. What happens to B? (Unchanged)
- Two parallel wires carry currents in the same direction. Attract or repel? (Attract)
Next: practice questions.