Question

When a rod of length $ l $ is rotated with angular velocity of $ \omega $ in a perpendicular field of induction $ B $ , about one end, the emf across its ends is

• A. $ Bl^{2}\omega $
• B. $ \frac{Bl^{2}\omega}{2} $
• C. $ Bl\omega $
• D. $ \frac{Bl\omega}{2} $

Answer 1

Answer: (B)

A conducting rod of length $l$ whose one end fixed, is rotated about the axis passing throug its fixed end and perpendicular to its length wit constant angular velocity $\omega$. Magnetic field $(B)$ perpendicular to the plane of the paper. Emf induced across the ends of the rod is $e=B An$

$=B \pi l^{2} n$
$=\frac{B l^{2} \pi}{T}$
$=\frac{1}{2} B l^{2} \omega$