(A) The magnetic flux through the coil at any time $t$ is given by $\phi = N A B \cos(\omega t)$.According to Faraday's law,the induced electromotive

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$\frac{N^2 A^2 B^2 \omega^2}{2 R}$

(A) The magnetic flux through the coil at any time $t$ is given by $\phi = N A B \cos(\omega t)$.According to Faraday's law,the induced electromotive force $(EMF)$ is $e = -\frac{d\phi}{dt} = N A B \omega \sin(\omega t)$.The peak $EMF$ is $e_0 = N A B \omega$.The peak current is $i_0 = \frac{e_0}{R} = \frac{N A B \omega}{R}$.The average power dissipated in a complete cycle is given by $P_{avg} = \frac{1}{2} e_0 i_0$.Substituting the values,$P_{avg} = \frac{1}{2} (N A B \omega) \left( \frac{N A B \omega}{R} \right) = \frac{N^2 A^2 B^2 \omega^2}{2 R}$.

Class 12 Physics Electromagnetic Induction Dynamic EMI and Periodic EMI

Easy

$A$ circular coil of resistance $R$,area $A$,and number of turns $N$ is rotated about its vertical diameter with angular speed $\omega$ in a uniform magnetic field of magnitude $B$. The average power dissipated in a complete cycle is:

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A
$\frac{N^2 A^2 B^2 \omega^2}{2 R}$
B
$\frac{B N A \omega}{R}$
C
$\frac{B N A \omega}{2 R}$
D
$\frac{N^2 A^2 B^2 \omega^2}{R}$

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Electromagnetic Induction

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Dynamic EMI and Periodic EMI

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$A$ ring of resistance $10 \ \Omega$,radius $10 \ cm$ and $100$ turns is rotated at a rate of $100$ revolutions per second about its diameter perpendicular to a uniform magnetic field of induction $10 \ mT$. The amplitude of the current in the loop will be nearly $....... \ A$. (Take: $\pi^2 = 10$)

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Write the equation for the maximum $emf$ in an $AC$ generator.

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$A$ circular coil of radius $8.0 \, cm$ and $20$ turns is rotated about its vertical diameter with an angular speed of $50 \, rad \, s^{-1}$ in a uniform horizontal magnetic field of $3.0 \times 10^{-2} \, T$. The maximum $emf$ induced in the coil will be $\ldots \ldots \ldots \times 10^{-2} \, V$ (rounded off to the nearest integer).

MediumJEE MAIN 2021

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$A$ planar loop made of wire is rotating in a uniform magnetic field. At time $t=0$,the plane of the loop is perpendicular to the magnetic field. If the loop is rotating about an axis passing through its plane with a period of $10 \; s$,at which of the following times will the induced electromotive force (emf) be maximum and minimum,respectively?

DifficultJEE MAIN 2020

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$A$ student pedals a stationary bicycle. The pedals of the bicycle are attached to a $100$ turn coil of area $0.10$ $m^2$. The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of $0.01$ $T$ perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil (in $V$)?

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$A$ circular coil of resistance $R$,area $A$,and number of turns $N$ is rotated about its vertical diameter with angular speed $\omega$ in a uniform magnetic field of magnitude $B$. The average power dissipated in a complete cycle is:

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$A$ ring of resistance $10 \ \Omega$,radius $10 \ cm$ and $100$ turns is rotated at a rate of $100$ revolutions per second about its diameter perpendicular to a uniform magnetic field of induction $10 \ mT$. The amplitude of the current in the loop will be nearly $....... \ A$. (Take: $\pi^2 = 10$)

Write the equation for the maximum $emf$ in an $AC$ generator.

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