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A solenoid has 2000 turns wound over a length of $0.30 \mathrm{~m}$. The area of its cross-section is $1.2 \times 10^{-3} \mathrm{~m}$. Around its central section, a coil of 300 turns is wound. If an initial current of $2 \mathrm{~A}$ in the solenoid is reversed in $0.25 \mathrm{~s}$, the emf induced in the coil is equal to
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Verified Answer
The correct answer is:
$4.8 \times 10^{-2} \mathrm{~V}$
Given,
$$
\begin{aligned}
N_1 & =2000 \\
L & =0.30 \mathrm{~m} \\
N_2 & =300
\end{aligned}
$$
$\frac{d i}{d t}=\frac{2-(-2)}{0.25}=\frac{4}{0.25} \mathrm{As}^{-1}$
$\begin{aligned} & A=1.2 \times 10^{-3} \mathrm{~m}^2 \\ & \text { Emf induced, } e=\frac{M d i}{d t}=\frac{\mu_0 N_1 N_2 A}{L} \times \frac{d i}{d t} \\ & \Rightarrow e=\frac{4 \pi \times 10^{-7} \times 2000 \times 300 \times 1.2 \times 10^{-3}}{0.30} \times \frac{4}{0.25} \\ & =4.8 \times 10^{-2} \mathrm{~V}\end{aligned}$
$$
\begin{aligned}
N_1 & =2000 \\
L & =0.30 \mathrm{~m} \\
N_2 & =300
\end{aligned}
$$
$\frac{d i}{d t}=\frac{2-(-2)}{0.25}=\frac{4}{0.25} \mathrm{As}^{-1}$
$\begin{aligned} & A=1.2 \times 10^{-3} \mathrm{~m}^2 \\ & \text { Emf induced, } e=\frac{M d i}{d t}=\frac{\mu_0 N_1 N_2 A}{L} \times \frac{d i}{d t} \\ & \Rightarrow e=\frac{4 \pi \times 10^{-7} \times 2000 \times 300 \times 1.2 \times 10^{-3}}{0.30} \times \frac{4}{0.25} \\ & =4.8 \times 10^{-2} \mathrm{~V}\end{aligned}$
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