(B) The induced electromotive force $(EMF)$ in the wire is given by $\varepsilon = Bvl$. Given: $B = 0.5 \, T$,$v = 2 \, ms^{-1}$,$l = 1 \, m$. $\vare

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(B) The induced electromotive force $(EMF)$ in the wire is given by $\varepsilon = Bvl$. Given: $B = 0.5 \, T$,$v = 2 \, ms^{-1}$,$l = 1 \, m$. $\varepsilon = 0.5 \times 2 \times 1 = 1 \, V$. The current in the circuit is $I = \frac{\varepsilon}{R} = \frac{1}{6} \, A$. The magnetic force acting on the wire is $F = BIl = 0.5 \times \frac{1}{6} \times 1 = \frac{0.5}{6} = \frac{1}{12} \, N$. The rate of work done (power) is $P = Fv = \frac{1}{12} \times 2 = \frac{1}{6} \, W$.

Class 12 Physics Electromagnetic Induction Motional EMI (Induced Parameter)

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$A$ wire of length $1 \, m$ is moving at a speed of $2 \, ms^{-1}$ perpendicular to its length and a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a circuit of resistance $6 \, \Omega$. The rate at which work is being done to keep the wire moving at constant speed is:

A
$\frac{1}{12} \, W$
B
$\frac{1}{6} \, W$
C
$\frac{1}{3} \, W$
D
$1 \, W$

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Electromagnetic Induction

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Motional EMI (Induced Parameter)

Statement-$I$: When a conducting rod moves in a uniform transverse magnetic field with a uniform speed which is perpendicular to its length,then a potential difference may develop across its ends.
Statement-$II$: In any conductor,free electrons and free positive ions are available.

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$A$ metal wire of length $2500 \ m$ is kept in east-west direction,at a certain height from the ground. If it falls freely on the ground,then the current induced in the wire when its speed is $10 \ m/s$ is (Resistance of wire $= 25 \ \Omega$,$g = 10 \ m/s^2$ and Earth's horizontal component of magnetic field $B_{H} = 2 \times 10^{-5} \ T$). (in $A$)

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$A$ $2 \; m$ wire is moving with a velocity of $1 \; m/s$ perpendicular to a magnetic field of $0.5 \; Wb/m^2$. The induced e.m.f. in it will be $... \; V$.

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$A$ rectangular wire loop of sides $8 \text{ cm}$ and $3 \text{ cm}$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3 \text{ T}$ directed normal to the plane of the loop. The emf developed across the cut, if the velocity of the loop is $2 \text{ cm s}^{-1}$ in a direction normal to the shorter side of the loop, will be:

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$A$ uniform magnetic field exists in the region given by $\vec{B} = 3\hat{i} + 4\hat{j} + 5\hat{k} \, T$. $A$ rod of length $L = 5 \, m$ placed along the $y$-axis is moved along the $x$-axis with a constant speed $v = 1 \, ms^{-1}$. The induced e.m.f. in the rod is ......... $V$.

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$A$ wire of length $1 \, m$ is moving at a speed of $2 \, ms^{-1}$ perpendicular to its length and a homogeneous magnetic field of $0.5 \, T$. The ends of the wire are joined to a circuit of resistance $6 \, \Omega$. The rate at which work is being done to keep the wire moving at constant speed is:

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Statement-$I$: When a conducting rod moves in a uniform transverse magnetic field with a uniform speed which is perpendicular to its length,then a potential difference may develop across its ends.Statement-$II$: In any conductor,free electrons and free positive ions are available.

$A$ $2 \; m$ wire is moving with a velocity of $1 \; m/s$ perpendicular to a magnetic field of $0.5 \; Wb/m^2$. The induced e.m.f. in it will be $... \; V$.

$A$ uniform magnetic field exists in the region given by $\vec{B} = 3\hat{i} + 4\hat{j} + 5\hat{k} \, T$. $A$ rod of length $L = 5 \, m$ placed along the $y$-axis is moved along the $x$-axis with a constant speed $v = 1 \, ms^{-1}$. The induced e.m.f. in the rod is ......... $V$.

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Statement-$I$: When a conducting rod moves in a uniform transverse magnetic field with a uniform speed which is perpendicular to its length,then a potential difference may develop across its ends.
Statement-$II$: In any conductor,free electrons and free positive ions are available.