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 Held 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                 \[F=i\,Bl\left( \frac{{{\mu }_{0}}}{2\pi }\frac{i}{b} \right)\]