question_answer

A wire PQRS carrying a current I run along three edges of a cube of side \[\ell \] as shown. There exists a uniform magnetic field of magnitude B along one of the sides of the cube. The magnitude of the force acting on the wire is ?

A) Zero                             

B) \[I\ell B\]

C) \[\sqrt{2}\,I\ell B\]          

D) \[2\ell B\]

Correct Answer: C

Solution :

[C] \[{{F}_{PQ}}=0\Rightarrow {{F}_{QR}}=I\ell B\] \[{{F}_{RS}}=I\ell B\] \[{{F}_{QR}}\] & \[{{F}_{RS}}\] are perpendicular to each other \[\therefore {{F}_{net}}=\sqrt{{{(I\ell B)}^{2}}+{{(I\ell B)}^{2}}}=\sqrt{2}I\ell B\]