A circular loop of radius a = 11 cm and N= 154 turns is fixed in the x-y plane. A spatially uniform magnetic field with only a z-component covers the entire area of the loop. The plot at the right shows Bz measured in tesla versus time t measured in seconds. The +z direction is OUT of the screen.

(a) Calculate the magnetic flux through the loop in the z-direction at the times indicated below. In each case, specify the direction by giving a positive value for flux in the +z direction and a negative value for flux in the -z direction.

At t = 1.0 s: Fm = T-m2

At t = 3.0 s: Fm = T-m2

At t = 5.0 s: Fm = T-m2 *
0 OK

At t = 6.5 s: Fm = T-m2

At t = 8.0 s: Fm = T-m2 *

At t = 9.5 s: Fm = T-m2

(b) Calculate the induced EMF (electromotive force) in the loop at the times specified below. In each case specify the sense of the EMF by giving a positive value for a counterclockwise EMF as viewed in the above figure; specify a clockwise sense by giving a negative value.

At t = 1.0 s: E = V

At t = 3.0 s: E = V *
0 OK

At t = 5.0 s: E = V

At t = 6.5 s: E = V *
0 OK

At t = 8.0 s: E = V

At t = 9.5 s: E = V *
0 OK

(c) Suppose now that the plane of the loop is tilted and then held fixed at an angle ? = 20° with respect to the x-y plane. The magnetic field remains in the z-direction and varies with time exactly as before.

Calculate the magnitude of the magnetic flux through the loop and the magnitude of the induced EMF in this case at t = 1 s.

|Fm| = T-m2

|E| = V

Question

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Physics: Principles with Applications

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