First slide

Magnetic flux and induced emf

Question

A flat circular coil 10 cm radius has 200 turns. The coil is connected to a capacitor of capacity 20 $μ$ F. It is placed in a uniform magnetic field which decreases at a rate of 0.01 tesla per second. The charge (in $μ C$ ) on the capacitor is_________.

Moderate

Solution

$\begin{array}{l} Q = e C, where e = induced emf = \frac{d ϕ}{d t} \\ Q = \frac{d ϕ}{d t} \cdot C = \frac{d}{d t} (N A B) C (∴ ϕ = N A B) \\ Q = N A \frac{d B}{d t} C = 200 \times π \times {(10 \times 10^{- 2})}^{2} (0.01) \times 20 \times 10^{- 6} \\ = 1.25 \times 10^{- 6} coulomb = 1.25 μ C \end{array}$

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