(B) The induced e.m.f. $e$ in a rotating rod is given by the rate of change of magnetic flux $\phi$ linked with the area swept by the rod.$e = \frac{d

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(B) The induced e.m.f. $e$ in a rotating rod is given by the rate of change of magnetic flux $\phi$ linked with the area swept by the rod.$e = \frac{d\phi}{dt} = B \frac{dA}{dt}$In one complete revolution,the rod sweeps an area $A = \pi l^2$.If the rod makes $f$ revolutions per second,the area swept per unit time is $\frac{dA}{dt} = f \cdot A = f \cdot \pi l^2$.Substituting this into the e.m.f. equation:$e = B \cdot (f \cdot \pi l^2)$Rearranging to solve for the frequency $f$ (number of revolutions per second):$f = \frac{e}{B \pi l^2}$

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

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$A$ metal rod of length $l$ rotates about one of its ends in a plane perpendicular to a magnetic field of induction $B$. If the e.m.f. induced between the ends of the rod is $e$,then the number of revolutions made by the rod per second is:

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A
$\frac{\pi l^2}{eB}$
B
$\frac{e}{B \pi l^2}$
C
$\frac{e}{B \pi^2 l}$
D
$\frac{B^2}{e \pi l}$

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Motional EMI (Induced Parameter)

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$A$ metal rod of length $l$ rotates about one of its ends in a plane perpendicular to a magnetic field of induction $B$. If the e.m.f. induced between the ends of the rod is $e$,then the number of revolutions made by the rod per second is:

Similar Questions

$A$ jet plane of wing span $20 \,m$ is travelling towards west at a speed of $400 \,ms^{-1}$. If the earth's total magnetic field is $4 \times 10^{-4} \,T$ and the dip angle is $30^{\circ}$ at that place, the voltage difference developed across the ends of the wing is (in $\,V$)

$A$ coil has $1000$ turns and $500 \text{ cm}^2$ as its area. The plane of the coil is placed at right angles to a magnetic induction field of $2 \times 10^{-5} \text{ Wb/m}^2$. The coil is rotated through $180^{\circ}$ in $0.2 \text{ s}$. The average emf induced in the coil,in $\text{mV}$,is

$A$ 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:

$A$ current carrying circular loop is perpendicular to a magnetic field of induction $10^{-4} \, T$. If the radius of the loop starts shrinking at a uniform rate of $2 \, mm/s$, then the emf induced in the loop at the instant, when its radius is $20 \, cm$ will be (in $\pi \, \mu V$)

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