(C) Consider a small radial segment of length $dx$ at a distance $x$ from the centre of the disc.The velocity of this segment is $v = \omega x$.The em

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(C) Consider a small radial segment of length $dx$ at a distance $x$ from the centre of the disc.The velocity of this segment is $v = \omega x$.The emf induced across this segment is given by $d\epsilon = B v dx = B \omega x dx$.Integrating this from the centre $(x=0)$ to the rim $(x=r)$, the total emf induced across the radius is:$\epsilon = \int_0^r B \omega x dx = \frac{1}{2} B \omega r^2$.Given: $B = 0.1 \ T$, $f = 10 \ \text{rev/s}$, so $\omega = 2 \pi f = 20 \pi \ \text{rad/s}$, and $r = 0.1 \ m$.Substituting the values:$\epsilon = \frac{1}{2} \times 0.1 \times 20 \pi \times (0.1)^2$$\epsilon = 0.1 \times 10 \pi \times 0.01$$\epsilon = 0.01 \pi \ V = 10 \pi \ mV$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

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$A$ copper disc of radius $0.1 \ m$ rotates about an axis passing through its centre and perpendicular to its plane with $10 \ \text{revolutions per second}$ in a uniform transverse magnetic field of $0.1 \ T$. The emf induced across the radius of the disc is

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A
$\frac{\pi}{10} \ V$
B
$\frac{2 \pi}{10} \ V$
C
$10 \pi \ mV$
D
$20 \pi \ mV$

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Motional EMI (Induced Parameter)

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$A$ metal conductor of length $1\;m$ rotates vertically about one of its ends at an angular velocity of $5\;rad/s$. If the horizontal component of the Earth's magnetic field is $0.2 \times 10^{-4}\;T$,then the $e.m.f.$ developed between the two ends of the conductor is:

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$A$ copper disc of radius $0.1 \ m$ rotates about an axis passing through its centre and perpendicular to its plane with $10 \ \text{revolutions per second}$ in a uniform transverse magnetic field of $0.1 \ T$. The emf induced across the radius of the disc is

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$A$ metal conductor of length $1\;m$ rotates vertically about one of its ends at an angular velocity of $5\;rad/s$. If the horizontal component of the Earth's magnetic field is $0.2 \times 10^{-4}\;T$,then the $e.m.f.$ developed between the two ends of the conductor is:

$A$ ceiling fan having $3$ blades of length $80 \ cm$ each is rotating with an angular velocity of $1200 \ rpm$. The magnetic field of Earth in that region is $0.5 \ G$ and the angle of dip is $30^{\circ}$. The $EMF$ induced across the blades is $N \pi \times 10^{-5} \ V$. The value of $N$ is:

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