Forces Between Parallel Wires
Forces Between Parallel Wires
- Two currents, two fields, two forces — a favourite question because it hides Newton's third law where intuition least expects it.
Why the wires push on each other
- The two-mark mechanism (9702/41/O/N/24 Q7(c)(i)): each wire sits in the magnetic field created by the other, and its current is perpendicular to that field, so a BIL force acts on it.
- Work the direction with Fleming's left-hand rule and a surprise appears: like currents attract, unlike currents repel — the opposite of charges and poles. The same physics pulls the turns of a current-carrying spring closer together, shortening it (9702/42/F/M/24 Q6(b)).
Worked example
The 2023 chain: force per unit length + Newton III
Wire P's field at wire Q is 2.6 mT, and Q carries 5.0 A. Find the force per unit length on Q. The field of Q back at P is only 1.5 mT — find the current in P (9702/41/M/J/23 Q6(c)).
- .
- By Newton's third law the force per unit length on P is the same 0.013 N m−¹, so .
Answer
Common mistake
Two Newton's-third-law traps from one 2024 question (9702/41/O/N/24 Q7(c)): doubling the current in X does not make the force on Y bigger than the force on X — the two forces stay equal and opposite whatever the currents. And reversing both currents leaves the force direction unchanged: the current and the field it sits in both flip, and two reversals cancel.