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:

$\frac{4}{5}πV$

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

$≃\frac{4}{5}πV$