Question

A conducting ring of radius $1m$ kept in a uniform magnetic field B of $0.01T$, rotates uniformly with an angular velocity 100 rad $s^{-1}$ with its axis of rotation perpendicular to B. The maximum induced emf in it is

• A. $1.5\pi V$
• B. $\pi V$
• C. $2\pi V$
• D. $0.5\pi V$
• E. $4\pi V$

Answer 1

Answer: (B)

$\pi V$

By magnetic induction
$B=\frac{\varphi }{A}$
or $\varphi =BA=\pi r^{2}B$
Given : $r=1m,$ $B=0.01T$ and $w=100rad/s$
$\varphi =\pi \times (1{)}^2\times 0.01=0.01\pi$
Maximum emf induced $E_{max}=BA\omega$
$E_{max}=0.01\pi \times 100=\pi volt$