question_answer

A triangular loop of side / carries a current I. It is placed in a magnetic field B, such that the plane of the loop is in the direction of B. The torque on the loop is:

A)  zero               

B)  \[IB{{l}^{2}}\]

C)  \[\sqrt{\frac{3}{2}}IB{{l}^{2}}\]

D)  \[\sqrt{\frac{3}{4}}IB{{l}^{2}}\]

Correct Answer: D

Solution :

Any closed current loop in a magnetic field has net force on it, is equal to zero however it may have a net torque (momentum) on it, due to couple of forces. Since,       \[\theta ={{90}^{o}}\] Hence  \[\tau =NIAB=I\times I\times \left( \frac{\sqrt{3}}{4}{{l}^{2}} \right)B=\frac{\sqrt{3I}}{4}{{l}^{2}}B\]