(B) The induced $emf$ across a rotating spoke is given by the formula $e = \frac{1}{2} B \omega \ell^2$.Given:$B = 0.40\,G = 0.40 \times 10^{-4}\,T$$l

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(B) The induced $emf$ across a rotating spoke is given by the formula $e = \frac{1}{2} B \omega \ell^2$.Given:$B = 0.40\,G = 0.40 \times 10^{-4}\,T$$l = 0.50\,m$$f = 120\,rev/min = \frac{120}{60}\,rev/s = 2\,Hz$Angular velocity $\omega = 2 \pi f = 2 \times \pi \times 2 = 4\pi\,rad/s$.Substituting the values:$e = \frac{1}{2} \times (0.40 \times 10^{-4}) \times (4\pi) \times (0.50)^2$$e = \frac{1}{2} \times 0.40 \times 10^{-4} \times 4 \times 3.14 \times 0.25$$e = 0.20 \times 10^{-4} \times 4 \times 3.14 \times 0.25$$e = 0.628 \times 10^{-4}\,V$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

Medium

$A$ wheel with ten metallic spokes,each $0.50\,m$ long,is rotated with a speed of $120\,rev/min$ in a plane normal to the Earth's magnetic field at the place. If the magnitude of the field is $0.40\,G$,the induced $emf$ between the axle and the rim of the wheel is equal to:

AIIMS 2010 All AIIMS

A
$1.256 \times 10^{-3}\,V$
B
$6.28 \times 10^{-4}\,V$
C
$1.256 \times 10^{-4}\,V$
D
$6.28 \times 10^{-5}\,V$

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Motional EMI (Induced Parameter)

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$A$ wheel with ten metallic spokes,each $0.50\,m$ long,is rotated with a speed of $120\,rev/min$ in a plane normal to the Earth's magnetic field at the place. If the magnitude of the field is $0.40\,G$,the induced $emf$ between the axle and the rim of the wheel is equal to:

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$A$ cycle wheel of radius $0.5 \; m$ is rotated with a constant angular velocity of $10 \; rad/s$ in a region of magnetic field of $0.1 \; T$ which is perpendicular to the plane of the wheel. The $EMF$ generated between its centre and the rim is.....$V$

$A$ metal rod $AB$ of length $50 \text{ cm}$ is moving at a velocity $8 \text{ ms}^{-1}$ in a magnetic field of $2 \text{ T}$. If the field is at $60^{\circ}$ with the plane of motion as shown in the figure,then the potentials $V_A$ and $V_B$ are related by

$A$ $10\,m$ long horizontal wire extends from North-East to South-West. It is falling with a speed of $5.0\,m/s$,at right angles to the horizontal component of the earth's magnetic field,which is $0.3 \times 10^{-4}\,Wb/m^2$. The value of the induced $emf$ in the wire is:

$A$ conductor loop of radius $R$ is present in a uniform magnetic field $B$ perpendicular to the plane of the ring. If the radius $R$ varies as a function of time $t$ as $R = R_0 + t$,the induced $e.m.f.$ in the loop is:

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