Q146 / 180 · JIPMER 2015 · Physics

The magnetic flux through each turn of a coil having 200 turns is given as $\left(t^2-2 t\right) \times 10^{-3}$ Wb , where $t$ is in second. The emf induced in the coil at $t=3 \mathrm{~s}$ is

  • A
    0.7 V
  • B
    1.2 V
  • Correct answer
    C
    0.8 V
  • D
    0.9 V

Solution

Given magnetic flux $\phi=\left(t^2-2 t\right) \times 10^{-3}$ On differentiating with recpect to time $t$ $\frac{d \phi}{d t}=(2 t-2) \times 10^{-3}$ At time $\quad t=3 \mathrm{~s}$ $\begin{aligned}\left|\frac{d \phi}{d t}\right|_{t=3 \mathrm{~s}} & =(2 \times 3-2) \times 10^{-3} \\ & =4 \times 10^{-3} \mathrm{~Wb} \mathrm{~s}^{-1} \\ \text { Now, }|e| & =N\left|\frac{d \phi}{d t}\right| \\ & =200 \times 4 \times 10^{-3} \\ & =800 \times 10^{-3}=0.8 \mathrm{~V}\end{aligned}$

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

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