question_answer

Two thin long parallel wires, separated by a distance d carry current i (amperes) each. The magnitude of the force per unit length exerted by one wire on the other is:

A)  \[{{\mu }_{0}}{{i}^{2}}/2\pi d\]

B)         \[{{\mu }_{0}}{{i}^{2}}/4\pi d\]

C)  \[{{\mu }_{0}}{{i}^{2}}/2\pi d\]

D)         \[{{\mu }_{0}}i/4\pi d\]

E)  \[{{\mu }_{0}}{{i}^{2}}/2\pi d\]

Correct Answer: A

Solution :

The force per unit length is \[\frac{F}{l}=\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}_{1}}{{i}_{2}}}{d}\] Given,        \[{{i}_{1}}={{i}_{2}}=i\] \[\therefore \]  \[\frac{F}{l}=\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}^{2}}}{d}\]