question_answer

A rigid conducting wire bent as shown, is released to fall freely in a horizontal magnetic field, which is perpendicular to the plane of the conductor. If magnetic field strength is B, then the emf induced across the points A and when it has fallen through a height h will be:

A)  \[B\ell \sqrt{2gh}\]                 

B) \[B\ell \sqrt{gh}\]

C) \[2B\ell \sqrt{gh}\]                  

D) \[2B\ell \sqrt{2gh}\]

Correct Answer: C

Solution :

The effective length is \[AC={{l}_{0}}=\sqrt{{{\ell }^{2}}+{{\ell }^{2}}}=\sqrt{2}\ell \] Induced emf \[=\varepsilon -B{{l}_{0}}v\] \[=B\sqrt{2}\ell \sqrt{2gh}=2B\ell \sqrt{gh}\] \[[\because \,v=\sqrt{2gh}]\] Hence, the correction option is [c].