Question

A wheel has three spokes and is in a uniform magnetic field perpendicular to its plane, with the axis of rotation of the wheel parallel to the magnetic field. When the wheel rotates with a uniform angular velocity $\omega$, the emf induced between the center and rim of the wheel is $e$. If another wheel having same radius but with six spokes is kept in the same field and rotated with a uniform angular velocity $\omega$/2, the emf induced between the center and the rim will be :

• A. $e$
• B. $e/2$
• C. $2e$
• D. $e/4$

Answer 1

The correct option is B $e/2$

E.m.f induced in this case is independent of no. of spokes. It is same in any case whether it is one spoke or infinite spoke (i.e. a disc). This is because emf generated in each spoke are connected in parallel between A & B.
$e=\frac{1}{2}B{R}^2\omega$
$e\propto \omega$
if $\omega$ is halved then $e$ is also halved.