A 200 turn circular coil of area $10^3\, cm^2$ rotates at 60 revolutions per minute in a uniform magnetic field of 0.02 T perpendicular to the axis of rotation of the coil. The maximum voltage induced in the coil is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{4}{5}πV$
To find the maximum voltage induced in the coil, one can use Faraday's law of induction,
$ε=NAB\sin(ωt)ω$
The maximum emf occurs when $(\sin ωt)=1$
and,
Angular velocity, $ω=2π$ × frequency in Hz
$=2π×\frac{60}{60}=2π\,rad/s$
Now,
$ε_{max}=200×10^3×10^{-4}×0.02×2π$
= 200 x 0.1 x 0.02 x $2π$
= 200 x 0.02 x $2π$
= 0.8π
$≃\frac{4}{5}πV$