Question

An annular circular brass disk of inner radius r and outer radius 'R' is rotating about an axis passing through its center and perpendicular to its plane with a uniform angular velocity $'\omega'$ in a uniform magnetic filed of induction B normal to the plane of the disk. The induced emf between the inner and outer edge of the annular disk is

• A. $\frac{B\omega(r^2+R^2)}{2}$
• B. $\frac{B\omega(R^2-r^2)}{2}$
• C. $\frac{B\omega(r-R)}{2}$
• D. $\frac{B\omega(r+R)}{2}$

Answer 1

Answer: (B)

$d ( emf )=- Bwxdx$
$emf =-\int\limits_{ r }^{ R } Bwxdx $
$=- Bw \int\limits_{ r }^{ R } \frac{ x ^{2}}{2} $
$= Bw \left(\frac{ R ^{2}- r ^{2}}{2}\right)$
Emf between inner and outer edge will be
$= Bw \left(\frac{ R ^{2}- r ^{2}}{2}\right)$