Question

An a.c. generator consists of a coil of $10,000$ turns and of area $100c{m}^2$. The coil rotates at an angular speed of $140$ rpm in a uniform magnetic field of $3.6\times {10}^{-2}$ T. Find the maximum value of the emf induced.

Answer 1

Number of turns $N=10000$ turns
Area of coil $A=100c{m}^2=0.01m^2$
Frequency $f=140rpm=\frac{140}{60}rps$
Angular speed $w=2\pi f=2\times \frac{22}{7}\times \frac{140}{60}=14.7rad/s$
Magnetic field $B=3.6\times {10}^{-2}T$
Maximum value of emf induced $E_{max}=NBAw$
$⟹$ $E_{max}=10000\times 3.6\times {10}^{-2}\times 0.01\times 14.7=52.9$ volts