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Faraday's Law

Magnetic fiel...

Question

Magnetic field through a coil having $200$ turns and cross - sectional area $0.04 m^{2}$ changes from $0.1 W b m^{- 2}$ to $0.04 W b m^{- 2}$ in $0.02 s e c$ . Find the induced emf

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Solution

$N = 200; A = 0.04 m^{2}; B_{1} = 0.1 W b m^{- 2}$
$B_{2} = 0.04 W b m^{- 2}; t = 0.02; e = ?$
$e = \frac{d ϕ}{d t} = \frac{- d (ϕ)}{d t}$
$e = - \frac{d}{d t} (N B A) = - N A \frac{d B}{d t} = - N A \frac{B_{2} - B_{1}}{d t}$
$= - 200 \times 4 \times 10^{- 2} \times \frac{(0.04 - 0.1)}{0.02}$
$e = 24 V$

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