Question

Two thin long parallel wires separated by a distance b are carrying a current i ampere each. The magnitude of the force per unit length exerted by one wire on the other is

• A. $\frac{\mu_0 i^2}{b^2}$
• B. $\frac{\mu_0 i^2}{2\pi b}$
• C. $\frac{\mu_0 i}{2\pi b}$
• D. $\frac{\mu_0 i}{2\pi b^2}$

Answer 1

Answer: (B)

Force per unit length between two wires carrying currents $i_1$ and $i_2$ at distance r is given by
$ \frac{F}{l}=\frac{\mu_0}{2\pi}\frac{i_1i_2}{r}$
Here,$ i_1=i_2=i\, \, \, \, and\, \, \, \, r=b$
$\therefore \frac{F}{l}=\frac{\mu_0i_2}{2\pi b}$
$\therefore $ Correct option is (b).