The area of a coil is 'A'. The coil is placed in a magnetic field which changes from ${ }^{\prime}…

The area of a coil is 'A'. The coil is placed in a magnetic field which changes from ${ }^{\prime} \mathrm{B}_{0^{\prime}}$ to ${ }^{\circ} 4 \mathrm{~B}_{0}{ }^{\prime}$ in time ${ }^{\prime} \mathrm{t}^{\prime}$. The magnitude of induced e.m.f. in the coil will be
  1. $\frac{3 \mathrm{AB}_{0}}{\mathrm{t}}$
  2. $\frac{4 \mathrm{AB}_{0}}{\mathrm{t}}$
  3. $\frac{3 \mathrm{~B}_{0}}{\mathrm{At}}$
  4. $\frac{4 \mathrm{~B}_{0}}{\mathrm{At}}$

Solution

$\frac{\mathrm{dB}}{\mathrm{dt}}=\frac{\mathrm{d}}{\mathrm{dt}}\left(4 \mathrm{B}_{0}-\mathrm{B}_{0}\right)=\frac{3 \mathrm{~B}_{0}}{\mathrm{t}}$ $e=\frac{d \phi}{d t}=\frac{d}{d t} A \cdot 3 B_{0}=\frac{3 B_{0} A}{t}$ .

Asked in: MHT CET 2020 (20 Oct Shift 2)

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