Question

(13 pts total) A long solenoid of radius a, carrying n turns per unit length, is looped by a wire with resistance R, as shown in the figure below. a. (7 pts) If the current in the loop is increasing at a constant rate (dl/dt-k), what current 1. flows in the loop, and which way (left or right) does it pass through the resistor? (6 pts) If the current I in the solenoid is constant, but the solenoid is pulled out of the loop and reinserted in the opposite direction, what total charge passes through the resistor? b.

Answer 1

Given that A solenoid with radius r. resistance R n turns per unit length (a) If current uparrow with constant rate what current flows in loop? its direction? Magnetic flux through the solenoid is phi^loop_mag = integral_turn integral B middot da Note where B = mu_0 pi nC magnetic field inside the loop = B pi r^2 (1) = mu_0 pi a^2 n l Therefore electromotive force sigma = -d phi^loop_mag/dt = -d mu_0 pi a^2 n l/dt \r\n - mu_) pi a^2 nh. Induced current I_end = Vertical-bar epsilon Vertical-bar /R = Vertical-bar mu_0 pi^2 an h Vertical-bar /R which in clockwise (b) When solenoid is pulled out & Re inserted in opposite direction. Then charge in total charge through the resistor magnetic flux: Delta Q^loop_mag = time interval Delta t = -t_f - t_0 Therefore Q^loop_mag (t_f) - phi^loop_mag (t_0) from note eq 1 = -B pi^2 - B pi a^2 = -mu_0 2 pi a^2 nl