A circular metal disc of area $3×10^-3 m^2$ is rotated at 50 rev/s about an axis through its center perpendicular to its plane. The disc is in a uniform magnetic field of flux density $5×10 ^-3T$ in the direction of the axle. What is the value of induced EMF?

Question Collected from Telegram Group.

Solution:

Area of metal disc (A) = 3 * 10^-3m²

Frequency (F) = 50 rev/s.

Magnetic field flux density (B) = 5 * 10^-3 Y

Volume of emf(E) = ?

We know, average velocity (V) = $\frac{{0 + {\rm{rw}}}}{2}$ = $\frac{{{\rm{rw}}}}{2}$.

Length(l) = r.

Induced emf (E) = BVl = B. $\frac{{{\rm{rw}}}}{2}$.r = B$\frac{{{{\rm{r}}^2}2{\rm{\pi f}}}}{2}$ = Br²πf.

= BAF(A = πr²)

= 5 * 10^-3 * 3 * 10^-3 * 50

= 7.5 * 10^-4V.

The maximum emf induced between the center of the axle and circumference.