Question

Ver ns is sureunded by a secend solenoid of radius b(ab), yth and n tuns per unit lungtih a) the current i bin the outer sodeneid is increasing ,Linear!ナwith tone s. that i, =«t where. ○く'u aconstant, what is +he. current ia in the ianer slenoid? what is the POgHnj vector in each reyion ce spa c) Evalvale each serm in Paying s teo (n disfocnthai Sorm ser the region rLb

Answer 1

Given that: A very long solenoid of length L, radius a, total resistance R_1 and N turns is surrounded by a second solenoid of radius b(a < b.), length 2 and n turns per unit length. Solenoid (i) L = length, R = resistance, a rightwardsdoublearrow Radius. Solenoid (ii) rightwardsdoublearrow L = length b = radius, I_b = current in (ii) (a) E_a = -d phi_0/dt = -d/dt (B_6 pi a^2) = -d/dt (mu_6 I_b 0 pi 0^2) {Because B = mu_0 nI_b/L = mu_0 nIb. \r\n E_a = -mu_0 n pi a^2 alpha E_a = -mu_0 alpha pi a^2 E_a = -mu_0 alpha n pi a^2 {-ve sign indicates that current flow would be opposite to outer solenoid} I_a = -mu_0 alpha pi a^2/R. (b) Mutual inductance = N_1 phi_21/I_b. < phi_21, live by 2 though > . phi_21 = B_b middot P_1a = mu_0 nI_b middot pi a^2 M = N mu_0 n pi a^2 M = mu_0 n pi a^2 rightarrow mutual indance.