question_answer

A current i flows in a circular coil of radius r. If the coil is placed in a uniform magnetic field B with its plane parallel to the field, magnitude of the torque that acts on the coil is  [MP PET 2001]

A)            Zero                                         

B)            \[2\pi \,r\,i\,B\]

C)            \[\pi \,{{r}^{2}}\,i\,B\]      

D)            \[2\pi \,{{r}^{2}}\,i\,B\]

Correct Answer: C

Solution :

                   As shown in the following figure, the given situation is similar to a bar magnet placed in a uniform magnetic field perpendicularly. Hence torque on it            \[\tau =MB\sin 90{}^\circ =(i\pi {{r}^{2}})B\]