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 \[\therefore {{F}_{net}}=\sqrt{{{(I\ell B)}^{2}}+{{(I\ell B)}^{2}}}=\sqrt{2}I\ell B\]