Question

The force per unit length between two infinitely long parallel conductors, with a gap of 2 cm between them, is 10 $\mu$N/m. When the gap is doubled, the force per unit length will be _____ $\mu$N/m (rounded off to one decimal place).

Hint:

For fixed currents in parallel wires, $F/L\propto 1/d$. Change the distance $\Rightarrow$ scale the force inversely.

Answer 1

Correct Answer: 4.9

For two long parallel conductors carrying fixed currents $I_1, I_2$, \[ \frac{F}{L}=\frac{\mu_0}{2\pi}\,\frac{I_1 I_2}{d}\,. \] Thus $\frac{F}{L}\propto \frac{1}{d}$. Doubling the separation $d$ halves the force per unit length: \[ \left(\frac{F}{L}\right)_{\!new}=\frac{1}{2}\left(\frac{F}{L}\right)_{\!old} =\frac{1}{2}\times 10=5.0\ \mu\text{N/m}. \]