During a 4.2 minute time interval the field uniformly changes at a constant rate

Question

During a 4.2 minute time interval the field uniformly changes at a constant rate, until a reversed field is reached equal in magnitude to the initial field. How much charge flows through the coil? Answer in units of C. A coil with N_1 = 23.6 turns and radius r_1 = 13 cm surrounds a long solenoid of radius r_2 = 2.35 cm and N_2/l_2 = n_2 = 1100 m^-1 (sec the figure below). The current in the solenoid changes as I = I_0 sin (omega t), where I_0 = 5 A and omega = 120 rad/s. Inside solenoid has N_2 turns Outside solenoid has N_1 turns What is the magnitude of the induced emf, epsilon_ AB, across the 23.6 turn coil at t = 1000 s? Answer in units of V. A circular coil enclosing an area of 142 cm^2 is made of 160 turns of copper wire as shown in the figure. A 6.3 Ohm resistor is inserted in the copper wire. Initially, a uniform magnetic field of magnitude 3.67 T points horizontally from left-to-right through the perpendicular plane of the coil. When viewed from the right the coil is wound counter-clockwise.

Explanation / Answer

given
time = 4.2 min
area = 142 cm^2
no.r of turns =160
resistence = 6.3 ohm
B = 3.67 T
The area is A = 142x 10^-4 m².

The change in magnetic flux is = AB = (142 x 10^-4) x (3.67 - (- 3.67 ))
= 0.104 Wb

The average induced emf is || = N / t = (160 turns x 0.104 Wb) / (4.2*60 s) = 0.066 V

The average current is I = / R = 0.066 / 6.3 = 0.0104 A

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