Faraday's law of Electromagnetic induction

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Question

A flat circular coil of 10 cm radius has 200 turns of wire. The coil is connected to a capacitor of $20 μ F$ placed in a uniform magnetic field whose induction decreases at a rate of $0 .01 T s^{- 1} .$ Find the charge on capacitor.

Moderate

Solution

$Q = eC, e = \frac{dϕ}{dt}$
$Q = \frac{dϕ}{dt} \cdot C = \frac{d}{dt} (NAB) C = NAC \frac{dB}{dt}$
$Q = 200 \times π \times 0 {.1}^{2} \times 10^{- 2} \times 20 \times 10^{- 6}$
$= 1 .25 \times 10^{- 6} C = 1 .25 μ C$

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