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:
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a
π2a2b2B2ω2R
b
π2a2b2B2ω22R
c
πabBωR
d
Zero
answer is B.
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Detailed 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