question_answer

Two thin long parallel wires separated by a distance b are carrying a current i amperes 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) \[\frac{{{\mu }_{0}}{{i}^{2}}}{2\pi {{b}^{2}}}\]

Correct Answer: B

Solution :

                It is experimentally observed that two current carrying conductors attract each other when current in them are in the same direction and repel, when in opposite direction. The force per unit length between the wires is given by \[\frac{F}{l}=\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}_{1}}{{i}_{2}}}{b}\] When   \[{{i}_{1}}={{i}_{2}}=i\]                                 \[\frac{F}{l}=\frac{{{\mu }_{0}}}{2\pi }=\frac{{{i}^{2}}}{b}\]