question_answer

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

A)  \[\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}^{2}}}{b}\]

B)  \[\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}^{2}}}{{{b}^{2}}}\]

C)  \[\frac{{{\mu }_{0}}}{2\pi }\frac{i}{b}\]

D)  \[\frac{{{\mu }_{0}}}{2\pi }\frac{i}{{{b}^{2}}}\]

Correct Answer: A

Solution :

The magnitude of magnetic field at any point on y due to current in X is given by    \[B=\frac{\mu }{2\pi }\frac{i}{b}\]    The force per unit length is \[F=i\,Bl=i\left( \frac{{{\mu }_{0}}}{2\pi }\frac{i}{b} \right)\]