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For the circuit shown below, the semi-circular part of the circuit is located in a3)magnetic field region, where the magnetic field is pointing in the z-direction perpendicular to the plane

of the loop, where positive z is out of the plane. The magnetic field varies in time as follows, B(t) = B,sin(omega,t)ē̟ . The radius of the loop, Ro, its resistance, R, as well as B, and w, are given. The emf ɛ, and the resistance r are also given. Work out the current in the circuit in terms of the given quantities. In addition(a)to carrying out the mathematical work, make sure to argue conceptually about the polarity of the induced emf for each part of the oscillation cycle of the magnetic field,and establish appropriate equivalent circuits. Explicitly show how the units in the expression work out to the proper units for the current. Graph the magnetic field, the magnetic flux, the induced emf and the current as(b)functions of time over a period of oscillation of the magnetic field. Is it possible for the current in the circuit to become zero, or to reverse direction?(c)Explain.

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