(A) The induced $emf$ $(\varepsilon)$ in a rod of length $l$ moving with velocity $v$ in a magnetic field $B$ is given by $\varepsilon = B l v$.To fin

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(A) The induced $emf$ $(\varepsilon)$ in a rod of length $l$ moving with velocity $v$ in a magnetic field $B$ is given by $\varepsilon = B l v$.To find the rate of increase of induced $emf$, we differentiate with respect to time $t$:$\frac{d\varepsilon}{dt} = B l \frac{dv}{dt}$.Since $\frac{dv}{dt} = a$ (acceleration), we have $\frac{d\varepsilon}{dt} = B l a$.Given: $B = 5 \times 10^{-4} \ Wb/m^2$, $l = 10 \ cm = 0.1 \ m$, $a = 5 \ m/s^2$.Substituting the values:$\frac{d\varepsilon}{dt} = (5 \times 10^{-4}) \times (0.1) \times (5) = 25 \times 10^{-4} \times 0.1 = 2.5 \times 10^{-4} \ V/s$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

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$A$ rod of $10 \ cm$ length is moving perpendicular to a uniform magnetic field of intensity $5 \times 10^{-4} \ Wb/m^2$. If the acceleration of the rod is $5 \ m/s^2$, then the rate of increase of induced $emf$ is . . . . . . .

GUJCET 2015 All GUJCET

A
$2.5 \times 10^{-4} \ V/s$
B
$25 \times 10^{-4} \ V/s$
C
$20 \times 10^{-4} \ V/s$
D
$20 \times 10^{-4} \ V/s^{-1}$

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Motional EMI (Induced Parameter)

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$A$ rod of $10 \ cm$ length is moving perpendicular to a uniform magnetic field of intensity $5 \times 10^{-4} \ Wb/m^2$. If the acceleration of the rod is $5 \ m/s^2$, then the rate of increase of induced $emf$ is . . . . . . .

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$A$ conducting bar moves on two conducting rails as shown in the figure. $A$ constant magnetic field $B$ exists into the page. The bar starts to move from the vertex at time $t=0$ with a constant velocity $v$. If the induced $\text{EMF}$ is $E \propto t^n$,then the value of $n$ 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:

$A$ 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

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