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Electrical Oscillations

A circular co...

Question

A circular coil of radius $8.0 c m$ and $20$ turns is rotated about its vertical diameter with an angular speed of $50 r a d s^{- 1}$ in a uniform horizontal magnetic field of magnitude $3.0 \times 10^{- 2} T$ . Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance $10 Ω$ , calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from?

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Solution

Maximum induced emf $e = N ω A B$ ;
$N = n o . o f t u r n s, ω = a n g u l a r s p e e d, A = A r e a o f c o i l, B = M a g n e t i c f i e l d$
$\Rightarrow e = 0.603 V$
Over a full cycle, the average emf induced in the coil is zero.
Maximum current, $I = e / R = 0.0603$
Average power loss due to joule heating is $P = \frac{e I}{2} = 0.018 W$

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