(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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Electromagnetic Induction

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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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An aircraft of wing span $40 \ m$ flies horizontally in the Earth's magnetic field of $5 \times 10^{-5} \ T$ at a speed of $500 \ m/s$. The electromotive force (e.m.f.) generated between the tips of the wings of the aircraft is: (in $V$)

$A$ 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

$A$ conducting rod of length $L$ rotates with angular speed $\omega$ in a uniform magnetic field of induction $B$ which is perpendicular to its motion. The induced emf developed between the two ends of the rod is

$A$ coil of area $80 \, cm^2$ and $50$ turns is rotating with $2000$ revolutions per minute about an axis perpendicular to a magnetic field of $0.05 \, T$. The maximum value of the e.m.f. developed in it is

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