Question

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

• A. rotate about an axis parallel to the wire
• B. move away from the wire or towards right
• C. move towards the wire
• D. remain stationary

Answer 1

Answer: (C)

move towards the wire

Force on a current carrying conductor is $F=\int i(\overrightarrow{dl}\times \overrightarrow{B})$
Current in the arms AD and CB are in opposite directions.
$\therefore$ for on any small segment on AD will have a counterpart on CB and force on CB will be opposite to that on AD.
As shown in the diagram, $\overrightarrow{F_2}=-\overrightarrow{F_4}$
Similarly force on AB and CD will be opposite but the magnitudes of the force are different due to different distance of AB and CD from the infinitely long wire.
$\therefore \overrightarrow{F_1}\ne -\overrightarrow{F_3}$
Since AB is closer to the infinite wire than CD, $\left|\overrightarrow{F_1}\right|>\left|\overrightarrow{F_3}\right|$
$\therefore$ the loop will move towards the wire.