A conducting wire form a semicircle ab of a radius 0.41 m . The wire has negligi
ID: 2118762 • Letter: A
Question
A conducting wire form a semicircle ab of a radius 0.41 m. The wire has negligible resistance. A 2.7-%u03A9 resister connects an end of the wire (b) to the center of the circle (c) as shown in Figure. A conducting rod connects the center (c) to the semicircle wire and sweeps around at an angular speed 12 rad/s in the counterclockwise direction (see Figure). The rod has negligible resistance. A uniform magnetic field perpendicular to the plane of the circle (into the plane) has a magnitude of
3.8 10-3T.(a) Find change in the magnetic flux during 0.12 s.
(b) Find the magnitude of the current induced in the loop.
Explanation / Answer
(a) Change in flux = B.dA = (3.8*10^ -3)*(0.0385) = 1.46*10^ -4
dA = (w*t/2*pi)*r^2 = (12*0.12/2*pi)*(0.41)^2 = 0.0385
(b) Emf induced = (change in flux)/dt = 1.46*10^ -4/0.12 = 1.22*10^ -3 V
Current induced = 1.22*10^ -3/2.7 = 4.52*10^ -4 Amp
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