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. $B{l}^2\omega$
• B. $\frac{B{l}^2\omega }{2}$
• 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 $e=BAn$

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