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 freque

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 :

TestHub · Accepted Answer

The expression for induced EMF in the rotating loop in uniform magnetic field is given by

$ϵ = N A B ω cos ω t$ The average power loss

$⟨ P ⟩ =< \frac{ϵ ^{2}}{R} >$ $=< \frac{A ^{2} B ^{2} ω ^{2} c o s ^{2} ω t}{R} >$

$< cos^{2} θ >= \frac{1}{2}$

$< P >= \frac{A ^{2} B ^{2} ω ^{2}}{R} (\frac{1}{2})$

$\Rightarrow< P >= \frac{π ^{2} a ^{2} b ^{2} B ^{2}}{2 R} (ω^{2})$

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