question_answer

A conducting rod of length 2l is rotating with constant angular speed w about its perpendicular bisector. A uniform magnetic field \[\overrightarrow{B}\] exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is [MP PET 2001]

A)            Bwl2                                         

B)            \[\frac{1}{2}B\omega {{l}^{2}}\]

C)            \[\frac{1}{8}B\omega {{l}^{2}}\]                                      

D)            Zero

Correct Answer: D

Solution :

                   Potential difference between O and A is  \[{{V}_{0}}-{{V}_{A}}=\frac{1}{2}B{{l}^{2}}\omega \] O and B is \[{{V}_{0}}-{{V}_{B}}=\frac{1}{2}B{{l}^{2}}\omega \] so \[{{V}_{A}}-{{V}_{B}}=0\]