A long solenoid of diameter 0.1, m has 2 time | vedclass

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(B) Given: $n = 2 	imes 10^4\, 	ext{turns/m}$,$I_i = 4\, A$,$I_f = 0\, A$,$N = 100$,$r = 0.01\, m$,$R = 10\pi^2\, \Omega$.The magnetic field inside

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$32\, \mu C$

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(B) Given: $n = 2 	imes 10^4\, 	ext{turns/m}$,$I_i = 4\, A$,$I_f = 0\, A$,$N = 100$,$r = 0.01\, m$,$R = 10\pi^2\, \Omega$.The magnetic field inside the solenoid is $B = \mu_0 n I$.Initial magnetic flux through the coil: $\phi_i = N B_i A = N (\mu_0 n I_i) (\pi r^2)$.Final magnetic flux through the coil: $\phi_f = N B_f A = N (\mu_0 n I_f) (\pi r^2) = 0$.Change in flux: $|\Delta \phi| = |\phi_f - \phi_i| = N \mu_0 n I_i \pi r^2$.$|\Delta \phi| = 100 	imes (4\pi 	imes 10^{-7}) 	imes (2 	imes 10^4) 	imes 4 	imes \pi 	imes (0.01)^2$.$|\Delta \phi| = 100 	imes 8\pi 	imes 10^{-3} 	imes \pi 	imes 10^{-4} = 32\pi^2 	imes 10^{-5}\, Wb$.Induced charge $q = \frac{|\Delta \phi|}{R} = \frac{32\pi^2 	imes 10^{-5}}{10\pi^2} = 3.2 	imes 10^{-6}\, C = 32\, \mu C$.

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