Question

A uniform thin rod of length L is moving in a uniform magnetic field $B_0$ such that velocity of its centre of mass is v and angular velocity is $\omega =\frac{4v}{L}$ Then

• A. e.m.f. between end P and Q of the rod is $B_{0}lv$
• B. end P of the rod is at higher potential than end Q of the rod
• C. end Q of the rod is at higher potential than end P of the rod
• D. the electrostatic field induced in the rod has same direction at all points along the length of rod

Answer 1

The correct option is B end P of the rod is at higher potential than end Q of the rod

The charges inside the rod move under the magnetic force given by

$\overrightarrow{F}=q(\overrightarrow{v}\times \overrightarrow{B})$

Thus the charges experience force towards end P. Hence end P is at higher potential.

EMF induced along a infinitesimal element along rod of length $dx$ is $dV=Bv\left(dx\right)$

$B\left(x\omega \right)dx$

Hence emf between points P and Q=${\int }_0^{L}B\left(x\omega \right)dx$

$=\frac{1}{2}B\omega L^2$

$=2BvL$