A solenoid 2m long, with 300 turns and radius R = 0.2 m carries a current of I =

Question

A solenoid 2m long, with 300 turns and radius R = 0.2 m carries a current of I = 3 A, clockwise as shown in the figure. A circular loop of copper wire with radius r = 0.03 m is situated concentrically within this solenoid (see figure) a) Calculate the magnetic flux through this inner wire loop. b) Now suppose you increase the solenoid current from 3.0 A to 5.0 A in 2.5 seconds. Calculate the induced voltage around the wire loop. c) Which way will the induced current flow? Explain why and indicate clearly in the figure.

Explanation / Answer

(A) B = u0 n I = u0 (N/L) I

B = (4pi x 10^-8) (300 / 2) (3)

B = 5.65 x 10^-4 T

flux = B A = (5.65 x 10^-4) (pi 0.03^2)

= 1.60 x 10^-6 Wb

(c) induced emf = rate of change of flux

e = (pi 0.03^2) (4pi x 10^-7 x 300/2)(2/2.5)

e = 4.26 x 10^-7 Volt

(D) couterclockwise

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