Question

Two parallel long wires carry the same current and repel each other with a force F per unit
length. If both these currents are doubled and the wire separation tripled, the force per unit
length becomes:
A. 2F/9
B. 4F/9
C. 2F/3
D. 4F/3
E. 6F

Answer 1

The force per unit length is given by the equation

$$ F=\frac{\mu_{0} I_{1} I_{2}}{2 \pi d} $$

or since the currents are equal:

$$ F=\frac{\mu_{0} I^{2}}{2 \pi d} $$

With the given changes, the new force (F') is

$$ F^{\prime}=\frac{\mu_{0}(2 \mathrm{I})^{2}}{2 \pi(3 \mathrm{~d})}=\frac{4}{3} \frac{\mu_{0} I^{2}}{2 \pi d}=\frac{4}{3} F $$