(C) The induced $emf$ across a rotating rod in a magnetic field is given by $\epsilon = \frac{1}{2} B \omega R^2$.Here,$B = H_E = 0.4 \; G = 0.4 \time

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(C) The induced $emf$ across a rotating rod in a magnetic field is given by $\epsilon = \frac{1}{2} B \omega R^2$.Here,$B = H_E = 0.4 \; G = 0.4 \times 10^{-4} \; T$.The angular velocity $\omega = 2 \pi \nu$,where $\nu = 120 \; rev/min = \frac{120}{60} \; rev/s = 2 \; rev/s$.So,$\omega = 2 \pi \times 2 = 4 \pi \; rad/s$.The length of the spoke $R = 0.5 \; m$.Substituting the values: $\epsilon = \frac{1}{2} \times (0.4 \times 10^{-4}) \times (4 \pi) \times (0.5)^2$.$\epsilon = 0.2 \times 10^{-4} \times 4 \pi \times 0.25 = 0.2 \times 10^{-4} \times \pi = 0.2 \times 3.14159 \times 10^{-4} \approx 6.28 \times 10^{-5} \; V$.The number of spokes is immaterial because the $emf$s across the spokes are in parallel.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

Difficult

$A$ wheel with $10$ metallic spokes,each $0.5 \; m$ long,is rotated with a speed of $120 \; rev/min$ in a plane normal to the horizontal component of the Earth's magnetic field $H_{E}$ at a place. If $H_{E} = 0.4 \; G$ at the place,what is the induced $emf$ between the axle and the rim of the wheel? $(1 \; G = 10^{-4} \; T)$

A
$1.56 \times 10^{-4} \; V$
B
$9.42 \times 10^{-5} \; V$
C
$6.28 \times 10^{-5} \; V$
D
$3.14 \times 10^{-5} \; V$

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

$A$ 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 . . . . . . .

MediumJEE MAIN 2025

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$A$ copper rod $AB$ of length $l$ is rotated about end $A$ with a constant angular velocity $\omega$. The electric field at a distance $x$ from the axis of rotation is

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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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$A$ $1.0 \ m$ metallic rod is rotated with an angular frequency $200 \ rad \ s^{-1}$ 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. The emf developed between the centre and the ring is . . . . . . . (in $V$)

EasyGSEB 2024

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$A$ circular wheel with $10$ spokes, with its plane vertical along East-West, is rotating about its natural axis with a uniform speed of $100$ revolutions per minute in the Earth's magnetic field. The radius of the wheel is $0.3 \, m$. If the $EMF$ induced between the centre of the wheel and the rim is $3 \pi \mu V$, what is the angle of dip at that place? (Vertical component of the Earth's magnetic field $B_{V} = 15 \mu T$)

DifficultAP EAMCET 2017

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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 . . . . . . .

$A$ copper rod $AB$ of length $l$ is rotated about end $A$ with a constant angular velocity $\omega$. The electric field at a distance $x$ from the axis of rotation is

$A$ 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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