Question

Hey, I know what will be fun! Let's put a solenoid inside another solenoid! The solenoid on the outside has a diameter of 5 cm, a length of 1.2 m, and 2400 turns. The inner solenoid has the same length, a diameter of 2 cm, and 50 turns. We send alternating current through the outer solenoid such that I = 1, cos(wt), where lo = 30 Amps, w = 2nf, and f= 60 Hz. a. What is the magnitude of the magnetic field inside the inner solenoid as a function of time? b. What is the voltage induced in the inner solenoid? c. Let's try it another way. We'll keep the outer solenoid the same, but we'll put another solenoid outside of it. The new solenoid will have a diameter of 10 cm and 50 turns. What is the voltage induced in this solenoid? d. Bigger is better, right? So let's make our new outer solenoid even bigger! It still has 50 turns, but now a diameter of 50 cm. What is the induced voltage?

Answer 1

outer solenoid 5cm = do la Inner Solenoid di 2 cm li ti2m ni = 50 1.2 m n 2400 I f Io coscit Goltz 30A To a) B; = Mono I B; 4 TTX20-? vloor 30 Cos (215x60th B = 2 I b) e= 9.05 cos (120TE) X10 -do dt T& ni 0 e - -ni A dB di dt 2 ni I di 2 dB li * 4 dt +501.3.14x 4x10.4 4 9,05x120 TT Sin(120074)x102 e * X 1.2 e 0.643 Sin (120 TT t) c ) field in the outer solenoid will be zero so flux Ø = Mono no I T8; 2) nol 0 = Mononi T8; 2 l I

Here no do 2400 50 ナ (ост ro dia 5 cm 4 TX107 X. 50 x 2400 X TTX (355)2x10 4x1.2 X Io coswt 1,066 x 10 cos (120 T - 2 of e 11 do dt 1 ? 4.02 Sin 120 Tt)] v
d) flux will only depend upon the inner solenoid current and radius so induced Voltage will be same as C.