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

The Correct Option is C

The maximum induced electromotive force (EMF) in a rotating coil is calculated using the formula:
ε_max = NABω
where: N represents the number of turns in the coil, A is the coil's area in square meters, B is the magnetic field strength in Tesla, and ω is the angular velocity in radians per second.

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

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

\(\text{Consequently, the maximum voltage induced in the coil is } \frac{4\pi V}{5}, \text{ which aligns with Option (3).}\)