(B) Given: Length of the rod,$l = 1.0 \; m$. Angular frequency,$\omega = 400 \; rad \; s^{-1}$. Magnetic field strength,$B = 0.5 \; T$. When a rod of

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(B) Given: Length of the rod,$l = 1.0 \; m$. Angular frequency,$\omega = 400 \; rad \; s^{-1}$. Magnetic field strength,$B = 0.5 \; T$. When a rod of length $l$ rotates about one of its ends in a uniform magnetic field $B$ with angular velocity $\omega$,the induced emf $(e)$ across its ends is given by the formula: $e = \int_{0}^{l} B v \; dr = \int_{0}^{l} B (\omega r) \; dr$ $e = B \omega \left[ \frac{r^2}{2} \right]_{0}^{l} = \frac{1}{2} B \omega l^2$ Substituting the given values: $e = \frac{1}{2} \times 0.5 \times 400 \times (1.0)^2$ $e = 0.25 \times 400 = 100 \; V$. Thus,the emf developed between the centre and the ring is $100 \; V$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

Medium

$A$ $1.0 \; m$ long metallic rod is rotated with an angular frequency of $400 \; rad \; s^{-1}$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. $A$ constant and uniform magnetic field of $0.5 \; T$ parallel to the axis exists everywhere. Calculate the emf developed between the centre and the ring. (in $; V$)

A
$50$
B
$100$
C
$200$
D
$400$

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

$A$ rectangular loop has a sliding connector $PQ$ of length $l$ and resistance $R \ \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2$ and $I$ are:

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The horizontal component of the earth's magnetic field at a place is $3 \times 10^{-4} \, T$ and the angle of dip is $53^\circ$. $A$ metal rod of length $0.25 \, m$ is placed in the north-south position and is moved at a constant speed of $10 \, cm/s$ towards the east. The emf induced in the rod will be ...... $\mu V$. (Given $\tan 53^\circ = 4/3$)

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$A$ uniform magnetic field exists in a region given by $\vec B = 3\hat i + 4\hat j + 2\hat k \, T$. $A$ conducting rod of length $5\,m$ is placed along the $y$-axis and is moved along the $x$-axis with a constant speed of $1\,m/s$. The $emf$ induced in the rod will be......$V$.

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$A$ coil of $n$ turns and area $A$ is placed with its axis parallel to a magnetic field. If the coil is rotated by $180^o$,the charge $Q$ induced in the circuit is given. If the resistance of the circuit is $R$,what is the magnitude of the magnetic field $B$?

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$A$ rectangular loop has a sliding connector $PQ$ of length $l$ and resistance $R \, \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2$ and $I$ are:

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$A$ rectangular loop has a sliding connector $PQ$ of length $l$ and resistance $R \ \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2$ and $I$ are:

$A$ uniform magnetic field exists in a region given by $\vec B = 3\hat i + 4\hat j + 2\hat k \, T$. $A$ conducting rod of length $5\,m$ is placed along the $y$-axis and is moved along the $x$-axis with a constant speed of $1\,m/s$. The $emf$ induced in the rod will be......$V$.

$A$ coil of $n$ turns and area $A$ is placed with its axis parallel to a magnetic field. If the coil is rotated by $180^o$,the charge $Q$ induced in the circuit is given. If the resistance of the circuit is $R$,what is the magnitude of the magnetic field $B$?

$A$ rectangular loop has a sliding connector $PQ$ of length $l$ and resistance $R \, \Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2$ and $I$ are:

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