11.6ProblemsProblem 30.15In figure 33, a stiff wire bent into a semicircle of radiusa= 2, cmis rotated at constant angularspeedf= 40rev/sin a uniform 20mTmagnetic field.What are the (a) frequency and (b)amplitude of the emf induced in the loop?Figure 33: Figure for problem 30.15The induced emf is generated by the changing magnetic flux through the circuit. In this case,the changing magnetic flux is not due to the magnetic field changing but rather the amount of areathough which the field passes is changing. Since the area oscillates back and forth at the frequencyf, the frequency of the emf must be the same.To find the amplitude of the emf we must do some calculations. We want to write down theflux through the loop as a function of time. Lets return to the definition of flux.ΦB=Z~B·d~A=BA1+ZB dA2cos
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