question_answer

Two long straight wires of length l lie parallel to one another and carry currents opposite to one another of magnitudes i­1 and i2 respectively. The force experienced by each of the straight wires is: (r is their distance of separation)

A)  repulsive and equal to \[\frac{{{\mu }_{0}}}{2\pi }\,\frac{{{l}^{2}}{{i}_{1}}{{i}_{2}}}{r}\] 

B)  repulsive and equal to \[\frac{{{\mu }_{0}}}{2\pi }\,\frac{l{{i}_{1}}{{i}_{2}}}{r}\]

C)  attractive and equal to \[\frac{{{\mu }_{0}}{{l}^{2}}{{i}_{1}}{{i}_{2}}}{2\pi {{r}^{2}}}\]

D)  attractive and equal to \[\frac{{{\mu }_{0}}l{{i}_{1}}{{i}_{2}}}{2\pi r}\]   

Correct Answer: B

Solution :

                 The force per unit length on either wire is given by \[F=\frac{{{\mu }_{0}}{{i}_{l}}.{{i}_{2}}}{2\pi r}\]                 Total force          \[F=\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}_{1}}{{i}_{2}}l}{r}\] When the current is flowing in the parallel wires in opposite direction, then the force will  be repulsive which will be equal to\[=\frac{{{\mu }_{0}}{{i}_{1}}{{i}_{2}}}{2\pi r}\]