Question

The distance between two thin long straight parallel conducting wires is $b$. On passing the same current $i$ in them, the force per unit length between them will be

• A. $\frac{{\mu }_{0}i}{2\pi b}$
• B. $\frac{{\mu }_0{i}^2}{2\pi }$
• C. $\frac{{\mu }_0{i}^2}{2\pi b}$
• D. zero

Answer 1

The correct option is C $\frac{{\mu }_0{i}^2}{2\pi b}$

The force between two long parallel conductors separated by distance r, is
$F=\frac{{\mu }_0\left(i_1\right)\left(i_2\right)}{2\pi r}$
Here, both conductors carry same current and they are separated by distance b, hence the force between them is
$F=\frac{{\mu }_0(i{)}^2}{2\pi b}$