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  4. An ideal solenoid of cross-sectional area 10-4 m 2 has 500 turns per metre. At the centre of this solenoid, another coil of 100 turns is wrapped closely around it. If the current in the coil changes from 0 to 2 A in 3.14 ms, the emf developed in the second coil is

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Q. An ideal solenoid of cross-sectional area $10^{-4}\, m ^{2}$ has $500 $ turns per metre. At the centre of this solenoid, another coil of $100$ turns is wrapped closely around it. If the current in the coil changes from $0$ to $2 \,A$ in $3.14 \,ms$, the emf developed in the second coil is

Electromagnetic Induction

Solution:

$M=\mu_{0} \,n_{1}\, n_{2} A$
$=4 \pi \times 10^{-7}(500)(100) \times 10^{-4}$
$\varepsilon=-\frac{M d i}{d t}=\frac{M(2)}{3.14}=4\, mV$