(A) The magnetic flux $\phi$ is given by $\phi = B A \cos \theta$. Since the plane is normal to the field,$\theta = 0^\circ$ and $\cos 0^\circ = 1$.Ch

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(A) The magnetic flux $\phi$ is given by $\phi = B A \cos \theta$. Since the plane is normal to the field,$\theta = 0^\circ$ and $\cos 0^\circ = 1$.Change in magnetic flux $\Delta \phi = (B_2 - B_1) A = (1 - 2) \times 0.01 = -0.01 \, Wb$.The induced electromotive force $(EMF)$ is given by Faraday's Law: $|\varepsilon| = |\frac{\Delta \phi}{\Delta t}| = \frac{0.01}{10^{-3}} = 10 \, V$.The heat produced $H$ is given by the formula $H = \frac{\varepsilon^2 \Delta t}{R}$.Substituting the values: $H = \frac{(10)^2 \times 10^{-3}}{0.01} = \frac{100 \times 10^{-3}}{0.01} = \frac{0.1}{0.01} = 10 \, J$.

Class 12 Physics Electromagnetic Induction Faraday's and Lenz's Law

Medium

$A$ physicist works in a laboratory where the magnetic field is $2 \, T$. She wears a necklace enclosing an area of $0.01 \, m^2$ in such a way that the plane of the necklace is normal to the field,and it has a resistance $R = 0.01 \, \Omega$. Because of a power failure,the magnetic field decays to $1 \, T$ in $10^{-3} \, s$. What is the total heat produced in her necklace in Joules?

A
$10$
B
$20$
C
$30$
D
$40$

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Electromagnetic Induction

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Faraday's and Lenz's Law

Three identical coils $C_1, C_2$ and $C_3$ are placed coaxially. $C_2$ is exactly midway between $C_1$ and $C_3$. $C_1$ carries current $I$ in an anti-clockwise direction, while $C_3$ carries current $I$ in a clockwise direction. An induced current flows through $C_2$ in a clockwise direction when:

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$A$ coil having effective area $A$ is held with its plane normal to a magnetic field of induction $B$. The magnetic induction is quickly reduced to $25 \%$ of its initial value in $1 \ s$. The e.m.f. induced in the coil (in volt) will be

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$A$ system $S$ consists of two coils $A$ and $B$. The coil $A$ carries a steady current $I$. The coil $B$ is suspended nearby as shown in the figure. If the system is heated,so as to raise the temperature of the two coils steadily,then:

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$A$ coil of resistance $400 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (Wb) linked with the coil varies with time $t$ $(s)$ as $\phi = 50t^2 + 4$,the current in the coil at $t = 2 \ s$ will be: (in $A$)

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$A$ circular coil of area $100 \,cm^2$ and $20$ turns is kept in a magnetic field of flux density $2 \,Wb/m^2$. It rotates from a position where its plane makes an angle of $30^{\circ}$ with the field to a position perpendicular to the field in a time $0.2 \,s$. Find the magnitude of the emf induced in the coil due to its rotation. (in $V$)

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Three identical coils $C_1, C_2$ and $C_3$ are placed coaxially. $C_2$ is exactly midway between $C_1$ and $C_3$. $C_1$ carries current $I$ in an anti-clockwise direction, while $C_3$ carries current $I$ in a clockwise direction. An induced current flows through $C_2$ in a clockwise direction when:

$A$ coil having effective area $A$ is held with its plane normal to a magnetic field of induction $B$. The magnetic induction is quickly reduced to $25 \%$ of its initial value in $1 \ s$. The e.m.f. induced in the coil (in volt) will be

$A$ system $S$ consists of two coils $A$ and $B$. The coil $A$ carries a steady current $I$. The coil $B$ is suspended nearby as shown in the figure. If the system is heated,so as to raise the temperature of the two coils steadily,then:

$A$ coil of resistance $400 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (Wb) linked with the coil varies with time $t$ $(s)$ as $\phi = 50t^2 + 4$,the current in the coil at $t = 2 \ s$ will be: (in $A$)

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