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)

$\frac{{\mu }_0{I}^2}{2\pi b}$

Given, $i_1=i_2=i$

$\therefore F=\frac{{\mu }_0{i}^{2}l}{2\pi b}$

Hence, force per unit length is $F=\frac{{\mu }_0{i}^2}{2\pi b}$