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

$ε = NAB ω \cos ω t$

The average power loss

$<P> = < \frac{ε^{2}}{R} >$ $= < \frac{A^{2} B^{2} ω^{2} \cos^{2} ω t}{R} >$

$< \cos^{2} θ > = \frac{1}{2}$

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

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

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