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
- A \(\frac{\mathrm{AB}}{2}\)
- B \(\frac{3 \mathrm{AB}}{4}\)
- C \(\frac{\mathrm{AB}}{4}\)
- D \(\frac{3 \mathrm{AB}}{8}\)
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:
\(\begin{aligned} & \mathrm{e}=\frac{\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{A} \frac{\mathrm{dB}}{\mathrm{dt}}=\mathrm{A} \frac{3}{4} \frac{\mathrm{B}}{1} \\ & \left(\because \mathrm{dB}=\frac{3}{4} \mathrm{~B}\right) \\ & \therefore \mathrm{E}=\frac{3 \mathrm{AB}}{4} \mathrm{~V}\end{aligned}\)
\(\begin{aligned} & \mathrm{e}=\frac{\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{A} \frac{\mathrm{dB}}{\mathrm{dt}}=\mathrm{A} \frac{3}{4} \frac{\mathrm{B}}{1} \\ & \left(\because \mathrm{dB}=\frac{3}{4} \mathrm{~B}\right) \\ & \therefore \mathrm{E}=\frac{3 \mathrm{AB}}{4} \mathrm{~V}\end{aligned}\)
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