question_answer

A rectangular loop carrying a current i is situated near a long straight wire such that the current carrying wire is parallel to one of the sides of a loop. If a steady current is established in a wire the loop will:

A)  rotate about an axis parallel to the wire

B)  move away from the wire

C)  move towards the wire

D)  remains stationary

Correct Answer: C

Solution :

                Two current carrying conductors attract each other when current is flowing in the same direction. The force of attraction is given by                 \[\frac{F}{l}=\frac{{{\mu }_{0}}}{2\pi }\frac{{{I}^{2}}}{a}\]where a is distance between the wires. In the given case, force of attraction between wires PQ and AD is                 \[{{F}_{A}}=\frac{{{\mu }_{0}}}{2\pi }\frac{{{I}^{2}}}{a}\] Force of repulsion (currents in opposite directions) between PQ and BC is                 \[{{F}_{R}}=\frac{{{\mu }_{0}}}{2\pi }\frac{{{I}^{2}}}{a}\] Since,           \[b>a\] \[\therefore \]      \[{{F}_{A}}>{{F}_{R}}\] Hence, loop moves towards the wire.