Question

A 200-turn circular coil of area 103cm2 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:

• A. $\quad \frac{2\pi V}{5} \\\\$
• B. $\quad \frac{\pi V}{4} \\\\$
• C. $\quad \frac{4\pi V}{5} \\\\$
• D. $\quad \frac{12\pi V}{5}$

Answer 1

Answer: (C)

$\quad \frac{4\pi V}{5} \\\\$

Answer 2

The maximum induced EMF in a rotating coil is given by the formula:
εmax = NABω
where:- N is the number of turns of the coil, A is the area of the coil in square meters, B is the magnetic field in Tesla, ω is the angular velocity in radians per second.

$\text{Given values: } N = 200, \, A = 10^3 \, \text{cm}^2 = 10^{-1} \, \text{m}^2, \, B = 0.02 \, \text{T}, \, \omega = 2\pi \times$ $\frac{60}{60} = 2\pi \, \text{rad/s}.\\\\$
$\text{Substituting the values into the formula:}$

$\varepsilon_{\text{max}} = 200 \times 10^{-1} \times 0.02 \times 2\pi = \frac{4\pi V}{5}$

$\text{Thus, the maximum voltage induced in the coil is } \frac{4\pi V}{5}, \text{ which corresponds to Option (3).}$