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A time-dependent, but spatially uniform magnetic field passes through a surface,S, defined by a circular conductive loop shown in Fig. 2 below. You should assume that the time-dependent magnetic field is given by B(t) = B. sin(wt)iz, where i, is the unit vector oriented along the z-axis.

Figure 2: A uniform magnetic field passing through the surface, S, defined by a conductive loop. (a) Calculate the time-dependent magnetic flux, Þ(t) = [ B. dŠ, passing through-the surface, S. [5 marks] (b) Show that the electromotive force, e, induced in the ring by this time-varying-magnetic flux, is given by \epsilon=-\pi R^{2} \omega B_{o} \cos (\omega t)

Assuming the following parameters calculate the peak electromotive force induced in the ring: R=10 cm, B = 1 mT, and f = 100 Hz. [7 marks] If the ring has a resistance of 102, what will the time-averaged dissipated power be? You are reminded that the root-mean-square (RMS) voltage is related to the peak voltage by VRMS = V peak/√2 and that the dissipated power is given by P = VRMS/R. [4 marks]

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