Problem 2. (4 points) Inducing an emf in a triangular loop inside a solenoid. A

Question

Problem 2. (4 points) Inducing an emf in a triangular loop inside a solenoid. A equilateral triangle, two-turn wire loop l = 1.44 cm on a side is placed inside a solenoid that has a circular cross section of radius r = 3 cm as shown in the end view of Fig. 2. The solenoid is 70 cm long and wound with 100 turns of wire. If the current in the solenoid is 5 A initially and reduced to zero in 4 s, what is the magnitude of the average induced emf in the triangular loop? (A) 20 nV (B) 30 nV (C) 40 nV (D) 68 nV

Explanation / Answer

B = u0 n I = u0 N I / L'

area of triangle = L (Lcos60)/2 = sqrt(3) L^2 / 4

= 0.433 L^2

flux = B A

emf = d(flux)/dt = (u0 N / L') (0.433 L^2) dI/dt

= (4pi x 10^-7)(100/0.70) (0.433 0.0144^2)(5/4)

= 20 x 10^-9 Volt

Ans(A) 20 nV

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