Question

In figure a $120-turn$ coil of radius $1.8$ cm and resistance $5.3\Omega$ is placed outside a solenoid. The current in the solenoid is $1.5\, A$ and it reduces to zero at a steady rate in $25\, ms$. What current (in mA) appears in the coil ? The number of turns per unit length of the solenoid is $220$ turns/cm and its diameter $D=3.2\, cm$.

Answer 1

The induced emf,$\left|e\right| = A \left(\frac{\Delta B}{\Delta t}\right)
= \left(\pi R\right)^{2}\mu_{0}n\begin{pmatrix}\Delta i\\ \Delta t\end{pmatrix}$
$=\pi \left(1.8 \times10^{-2}\right)^{2} \times\left(4\pi \times10^{-7}\right) \times220 \times10^{2}$
$\times\left(\frac{1.5}{25 \times10^{-3}}\right) = 68.6\,mV$
Current,$i =\frac{e}{R} =30 \,mA$