The picture shows a uniform, 3.0-T magnetic field that is normal to the plane of

Question

The picture shows a uniform, 3.0-T magnetic field that is normal to the plane of a conducting loop with a resistance of 1.5 O and a radius of 0.024 m. The magnetic field is directed out of the paper as shown. NOTE: The area of the non-circular portion of the wire is considered negligible compared to that of the circular loop. ~What is the magnitude of the average induced emf in the loop if the magnitude of the magnetic field is doubled in 0.4 s? a)0.43 V b)0.65 V c)0.014 V d)0.027 V e) 0.038 V ~What is the average current around the loop if the magnitude of the magnetic field is doubled in 0.4 s? a)2.8 x 10^-3 A, clockwise b)4.5 x 10^-3 A, clockwise c)4.5 x 10^-3 A, counterclockwise d)9.0 x 10^-3 A, clockwise ~If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, what is the magnitude of the average induced emf in the loop? a)8.6 x 10^-3 V b)9.8 x 10^-2 V c)2.7 x 10^-2 V d)5.4 x 10^-2 V e)6.4 x 10^-2 V ~ If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 x, at what rate is energy dissipated in R? a)1.8 x 10^-2 W b)3.6 x 10^-2 W c)3.8 x 10^-3 W d)2.7 x 10^-4 W e)4.9 x 10^-4 W

Explanation / Answer

B = 3.0-T, R = 1.5 O, r = 0.024 m. area A = pi*r^2 = 1.81*10^-3 m^2 ~What is the magnitude of the average induced emf in the loop if the magnitude of the magnetic field is doubled in t = 0.4 s? change in magnetic flux = (2B - B)*A = BA average induced emf = BA/t = 0.014 V answer: c) ~What is the average current around the loop if the magnitude of the magnetic field is doubled in 0.4 s? average current = average induced emf/R = 0.014/1.5 = 9.0 x 10^-3 A note flux is increasing, so current is clockwise answer: d) ~If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in t = 0.2 s, what is the magnitude of the average induced emf in the loop? change in magnetic flux = (0 - B)*A = -BA magnitude = BA average induced emf = BA/t = 0.027 V answer: c) ~ If the magnetic field is held constant at 3.0 T and the loop is pulled out of the region that contains the field in 0.2 s, at what rate is energy dissipated in R? energy dissipated in R = emf^2/R = 4.9 x 10^-4 W answer: e)

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