A circular coil of radius 10 cm is placed in a uniform magnetic field… | JEE Main 2020 (2 Sep, Shift 1)

Q29JEE Main 2020 · 2 SEP · SHIFT 1Medium

Rotating Conductors & AC Generator

A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 $\times$ 10–5 T with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in 0.2 s. The maximum value of EMF induced (in $\mu$ V) in the coil will be close to the integer _______.

Numerical answer type. Work it out, then open the answer.

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Answer: 15

Half rotation in 0.2 s, so $T = 0.4\text{ s}$ and $\omega = \frac{2\pi}{0.4} = 5\pi$ rad/s.
$A = \pi(0.1)^2 = 0.01\pi\text{ m}^2$
$e_0 = BA\omega = 3\times10^{-5} \times 0.01\pi \times 5\pi = 1.5\times10^{-6}\pi^2$
$e_0 \approx 1.48\times10^{-5}\text{ V} \approx 15\ \mu\text{V}$

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