First slide

Magnetic flux and induced emf

Question

A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be
quadrupled and the wire radius halved, the electrical power dissipated would be,

Moderate

A

halved
B

the same
C

doubled
D

quadrupled

Solution

$Power P = \frac{ε^{2}}{R} hence ε = - (\frac{d φ}{d t}) where φ = N B A$
$\begin{array}{l} ∴ ε = - N A (\frac{d B}{d t}) Also R \propto \frac{l}{r^{2}} \propto \frac{N}{r^{2}} \\ where R = resistance, r = radius, l = length \\ ∴ P \propto \frac{N^{2} r^{2}}{N} \propto N r^{2} \\ N b e c o m e s q u a d r u p l e d a n d r a d i u s i s h a l v e d . \\ \Rightarrow \frac{P_{1}}{P_{2}} = 1 \end{array}$

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