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MHT CET · Physics · Electromagnetic Induction

A coil having effective area ' \(\mathrm{A}\) ' is held with its plane normal to a magnetic field of induction ' \(\mathrm{B}\) '. The magnetic induction is quickly reduced to \(25 \%\) of its initial value in 1 second. The e.m.f. induced in the coil (in volt) will be

  1. A \(\frac{\mathrm{AB}}{2}\)
  2. B \(\frac{3 \mathrm{AB}}{4}\)
  3. C \(\frac{\mathrm{AB}}{4}\)
  4. D \(\frac{3 \mathrm{AB}}{8}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{3 \mathrm{AB}}{4}\)

Step-by-step Solution

Detailed explanation

Induced emf is equal to change in flux per unit time:
\(\begin{aligned} & \mathrm{e}=\frac{\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{A} \frac{\mathrm{dB}}{\mathrm{dt}}=\mathrm{A} \frac{3}{4} \frac{\mathrm{B}}{1} \\ & \left(\because \mathrm{dB}=\frac{3}{4} \mathrm{~B}\right) \\ & \therefore \mathrm{E}=\frac{3 \mathrm{AB}}{4} \mathrm{~V}\end{aligned}\)