(C) The motional electromotive force $(EMF)$ induced in a rod of length $l$ rotating about one end with angular velocity $\omega$ in a uniform magneti

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(C) The motional electromotive force $(EMF)$ induced in a rod of length $l$ rotating about one end with angular velocity $\omega$ in a uniform magnetic field $B$ is given by $\varepsilon = \frac{1}{2} B \omega l^2$.Here,the ring rotates about point $O$. Any chord of length $l$ passing through $O$ acts as a rotating rod.The distance $OP = \sqrt{a^2 + a^2} = \sqrt{2}a$. Thus,$V_P - V_O = \frac{1}{2} B \omega (\sqrt{2}a)^2 = B \omega a^2$.The distance $OQ = 2a$. Thus,$V_Q - V_O = \frac{1}{2} B \omega (2a)^2 = 2 B \omega a^2$.Comparing these with the options,option $C$ is correct.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the magnitude of potential differences.

A
$V_P - V_O = \frac{1}{2} B\omega a^2$
B
$V_P - V_Q = \frac{1}{2} B\omega a^2$
C
$V_Q - V_O = 2B\omega a^2$
D
$V_P - V_R = 2B\omega a^2$

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Class 12

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

$A$ horizontal loop $abcd$ is moved across the pole pieces of a magnet as shown in the figure with a constant speed $v$. When the edge $ab$ of the loop enters the pole pieces at time $t = 0 \text{ s}$,which one of the following graphs correctly represents the induced emf in the coil?

Medium

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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:

MediumAIIMS 2010

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$A$ 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:

DifficultJEE MAIN 2024

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$A$ 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

DifficultAP EAMCET 2003

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$A$ circular disc of radius $0.1 \ m$ is rotating about its axis at a frequency of $10 \ rev/s$ in a uniform magnetic field of $0.1 \ T$ directed perpendicular to the disc. Calculate the induced $emf$ between the center and the rim of the disc.

Easy

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$A$ horizontal loop $abcd$ is moved across the pole pieces of a magnet as shown in the figure with a constant speed $v$. When the edge $ab$ of the loop enters the pole pieces at time $t = 0 \text{ s}$,which one of the following graphs correctly represents the induced emf in the coil?

$A$ 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:

$A$ 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

$A$ circular disc of radius $0.1 \ m$ is rotating about its axis at a frequency of $10 \ rev/s$ in a uniform magnetic field of $0.1 \ T$ directed perpendicular to the disc. Calculate the induced $emf$ between the center and the rim of the disc.

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