Q94 / 120 · VITEEE 2011 · Physics

A solenoid has 2000 turns wound over a length of $0.30 \mathrm{~m}$. The area of its cross-section is $1.2 \times 10^{-3} \mathrm{~m}^{2}$. Around its central section, a coil of 300 turn is wound. If an initial current of $2 \mathrm{~A}$ in the solenoid is reversed in $0.25 \mathrm{~s}$, then the emf induced in the coil is

  • A
    $6 \times 10^{-4} \mathrm{~V}$
  • B
    $4.8 \times 10^{-3} \mathrm{~V}$
  • C
    $6 \times 10^{-2} \mathrm{~V}$
  • Correct answer
    D
    $48 \mathrm{mV}$

Solution

Induced emfe $=M \frac{d i}{d t}$ $=\frac{\mu_{0} N_{1} N_{2} A}{l} \cdot \frac{d i}{d t}$ $=\frac{4 \pi \times 10^{-7} \times 2000 \times 300 \times 1.2 \times 10^{-3}}{0.30}$ $=48.2 \times 10^{-3} \mathrm{~V}=48 \mathrm{mV}$

Hence, the correct answer is option: 'D'.

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