A 100 turns coil of area of cross section $200 \mathrm{~cm}^{2}$ having $2 \Omega$ resistance is hel

Question

A 100 turns coil of area of cross section $200 \mathrm{~cm}^{2}$ having $2 \Omega$ resistance is held perpendicular to a magnetic field of 0.1 T, If it is removed from the magnetic field in one second, the induced charges produced in it is\

Professor PC Thomas Classes · Answer

Here, area of cross section\ $\mathrm{A}=200 \mathrm{~cm}^{2}=200 	imes 10^{-4} \mathrm{~m}^{2}$\ Number of turn $=\mathrm{N}=100$\ Resistance, $\mathrm{R}=2 \Omega$\ Initial magnetic flux linked with the coil is\ $\phi_{\mathrm{i}}=\mathrm{BA} \cos 	heta$\ $=0.1 	imes 200 	imes 10^{-4} 	imes \cos 0^{\circ}$\ $=2 	imes 10^{-3} \mathrm{~Wb}$\ Final magnetic flux linked with the coil is\ $\phi_{\mathrm{f}}=0 \quad(\because \mathrm{~B}=0)$\ $	herefore$ Induced emf in the coil is, $\varepsilon=-\frac{\mathrm{N} \Delta \phi}{\Delta \mathrm{t}}$\ $=\frac{-\mathrm{N}\left(\phi_{\mathrm{f}}-\phi_{\mathrm{i}}ight)}{\Delta \mathrm{t}}$\ $=\frac{-100\left(0-2 	imes 10^{-3}ight)}{1}=2 	imes 10^{-1} \mathrm{~V}=0.2 \mathrm{~V}$\ Induced current in the coil is\ $\mathrm{I}=\frac{\varepsilon}{\mathrm{R}} \frac{0.2 \mathrm{~V}}{2 \Omega}=0.1 \mathrm{~A} \mathrm{I}=$\ Induced charge in coil, $\mathrm{q}=\mathrm{It}$\ $=0.1 	imes 1=0.1 \mathrm{C}$