A very long, tightly-wound solenoid has a circular cross section of radius r = 2

Question

A very long, tightly-wound solenoid has a circular cross section of radius r = 2.7 cm (only a portion of the very long solenoid is shown in the figure). The magnetic field outside the solenoid is negligible. Throughout the inside of the solenoid the magnetic field B is uniform, out of the page as shown, but varying with time t: B = [0.07 + 0.03t2] tesla. Surrounding the circular solenoid is a loop of N = 7 turns of wire in the shape of a rectangle 11 cm high by 15 cm wide. The total resistance of the 7-turn loop is 0.1 ohm.

Explanation / Answer

Here ,

magnetic field , B = 0.07 + 0.03 t^2

radius , r = 2.7 cm = 0.027 m

resistance , R = 0.1 Ohm

current induced = N * A * dB/dt/R

current = 7 * pi * 0.027^2 * d/dt(0.07 + 0.03 * t^2)/0.1

current = 0.1603 * 0.06 * t

current = 9.617 *10^-3 * t

the current in the loop is 9.617 *10^-3 * t

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