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
$\frac{F}{l}=\frac{{\mu }_0}{2\pi }\frac{i_1{i}_2}{r}$
Here,$i_1=i_2=iandr=b$
$\therefore \frac{F}{l}=\frac{{\mu }_0{i}_2}{2\pi b}$
$\therefore$ Correct option is (b).