First slide
Magnetic flux and induced emf
Question

An elliptical loop having resistance R, of semi major axis a, and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency  ω, the average power loss in the loop due to Joule heating is:

Moderate
Solution

Magntic flux=ϕ=BAcosωt=B(πab)cosωtInduced emf =V=dϕdt=Bπabω sinωtPeak emf=V0=BπabωRms emf =Vrms=V02=Bπabω2 Average Power =P=Vrms2R=Bπabω221R

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