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

$Power P = \frac{e^{2}}{R}; hence e = - (\frac{dϕ}{dt}) where ϕ = NBA$
$∴e=−NA (\frac{dB}{dt}) Also R \propto \frac{l}{r^{2}}$
As number of turns increases, the length of wire also increase.
$l \propto N$
Where R = resistance, r = radius, l = Length
$∴ P \propto \frac{N^{2} r^{2}}{l} \propto {Nr}^{2} \Rightarrow \frac{P_{1}}{P_{2}} = 1$

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