(A) Given: Length $l = 10 \, cm = 0.1 \, m$,Magnetic field $B = 1.0 \, T$,Velocity $v = 20 \, cm/s = 0.2 \, m/s$,Angle $\theta = 60^\circ$.The motiona

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(A) Given: Length $l = 10 \, cm = 0.1 \, m$,Magnetic field $B = 1.0 \, T$,Velocity $v = 20 \, cm/s = 0.2 \, m/s$,Angle $\theta = 60^\circ$.The motional $emf$ induced in a conductor moving in a magnetic field is given by $E = B v l \sin \theta$,where $\theta$ is the angle between the velocity vector and the length of the wire.Substituting the values:$E = 1.0 \times 0.2 \times 0.1 \times \sin 60^\circ$$E = 0.02 \times \frac{\sqrt{3}}{2}$$E = 0.01 \times 1.732$$E = 0.01732 \, V$$E = 17.32 \times 10^{-3} \, V$.Thus,the induced $emf$ is approximately $17 \times 10^{-3} \, V$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

Medium

$A$ wire of length $10 \, cm$ translates in a direction making an angle of $60^\circ$ with its length. The plane of motion is perpendicular to a uniform magnetic field of $1.0 \, T$ that exists in the space. Find the $emf$ induced between the ends of the rod if the speed of translation is $20 \, cm/s$.

A
$17 \times 10^{-3} \, V$
B
$27 \times 10^{-3} \, V$
C
$7 \times 10^{-3} \, V$
D
$57 \times 10^{-3} \, V$

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

$A$ metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region,the $e.m.f.$ induced across the ends of the rod is

MediumJEE MAIN 2013

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$A$ $10 \, m$ wire kept in the east-west direction is falling with a velocity of $5 \, m/s$ perpendicular to the magnetic field of $0.3 \times 10^{-4} \, Wb/m^2$. The induced e.m.f. across the terminals of the wire will be:

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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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$A$ straight conductor of length $0.6 \, m$ is moved with a speed of $10 \, ms^{-1}$ perpendicular to a magnetic field of induction $1.2 \, Wb \cdot m^{-2}$. The induced e.m.f. across the conductor is (in $V$)

EasyMHT CET 2021

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$A$ long metal rod of length $L$ completes the circuit as shown. The area of the circuit is perpendicular to the magnetic field $B$. The total resistance of the circuit is $R$. The force needed to move the rod in the direction as shown with a constant speed $V$ is:

EasyMHT CET 2020

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$A$ metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region,the $e.m.f.$ induced across the ends of the rod is

$A$ $10 \, m$ wire kept in the east-west direction is falling with a velocity of $5 \, m/s$ perpendicular to the magnetic field of $0.3 \times 10^{-4} \, Wb/m^2$. The induced e.m.f. across the terminals of the wire will be:

$A$ 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:

$A$ straight conductor of length $0.6 \, m$ is moved with a speed of $10 \, ms^{-1}$ perpendicular to a magnetic field of induction $1.2 \, Wb \cdot m^{-2}$. The induced e.m.f. across the conductor is (in $V$)

$A$ long metal rod of length $L$ completes the circuit as shown. The area of the circuit is perpendicular to the magnetic field $B$. The total resistance of the circuit is $R$. The force needed to move the rod in the direction as shown with a constant speed $V$ is:

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