Problem 15 Su ppose the solenoid in the fig has a length of 50 cm with 1000 turn
ID: 3281416 • Letter: P
Question
Problem 15 Su ppose the solenoid in the fig has a length of 50 cm with 1000 turns. The radius of the solenoid is r2-2 cm. A conducting circular loop of radius r1 1 cm is placed at the center of the solenoid with its axis the same as that of the solenoid as shown In the figure. The resistance of the circular loop is R.5 If the solenoid carries a constant current of I-20 A a) What is magnetic field at the center of the I-20 A eolenokd solenoid (vector)? 12cm = 0.05 T (-1) b) If a current of 0.1 A passes through the loop as shown, what is the torque on the loop and its energy?Explanation / Answer
a)
for the magnetic field at the center of the solenoid
B = u0 * N * I/L (-i)
B = 4pi *10^-7 * 1000 * 20/.50
B = 0.050 T (-i)
the magnetic field is 0.050 T (-i)
b)
magnetic moment , u = pi r^2 * I
u = pi * 0.01^2 * 0.1 = 3.14 *10^-5 (- i )A.m^2
torque on the loop = u X B
torque on the loop = 3.14 *10^-5 (- i ) X 0.050 T (-i)
torque on the loop = 0 N.m
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for the energy
energy stored in the loop = - u . B
energy stored in the loop = -3.14 *10^-5 * 0.050
energy stored in the loop = -1.57 *10^-6 J