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 + 0.03t^2] tesla. Surrounding the circular solenoid is a loop of N = 3 turns of wire in the shape of a rectangle 9 cm high by 19 cm wide. The total resistance of the 3-turn loop is 0.1 ohm. (a) At t = 3.4 seconds, what is the direction of the current in the 3-turn loop? clockwise there is no current in the loop counter-clockwise (b) At t = 3.4 seconds, what is the magnitude of the current in the 3-turn loop? A

Explanation / Answer

V = (.06*3.4)*(.027^2*pi)*3= 0.0014016
I = 0.0014016/.1= 0.014 A

The amplitude of the current in the 3 turn loop is 0.014 A.

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