question_answer

Two parallel wires in free space arc 10 cm apart, and each carries a current of 10A, in the same direction. The force, one wire exerts on the other, per metre of length, is :

A) \[2\times {{10}^{-7}}N,\]repulsive

B) \[2\times {{10}^{-7}}N,\]attractive

C) \[2\times {{10}^{-4}}N,\]repulsive

D) \[2\times {{10}^{-4}}N,\]attractive

Correct Answer: D

Solution :

                The force per unit length of wire 2 due to wire 1 is, \[\frac{F}{l}=\frac{{{\mu }_{0}}}{2\pi }\frac{{{i}_{1}}{{i}_{2}}}{r}\] Making substitution, we obtain                                 \[\frac{F}{l}=\frac{4\pi \times {{10}^{-7}}}{2\pi }\times \frac{10\times 10}{10\times {{10}^{-2}}}\]                 \[=2\times {{10}^{-4}}N/m\] Since, currents are flowing in same direction so, force produced between them will be attractive. NOTE: If the currents are flowing in opposite direction, the force between them will be repulsive.