An infinitely long straight wire carrying current $I$,an open rectangular loop,and a conductor $C$ with a sliding connector are located in the same plane,as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self-inductance of the loop are negligible. The induced current in the loop,as a function of separation $r$ between the connector and the straight wire,is:

  • A
    $\frac{\mu_{0}}{\pi} \frac{ Ivl }{ Rr }$
  • B
    $\frac{\mu_{0}}{2 \pi} \frac{ Ivl }{ Rr }$
  • C
    $\frac{2 \mu_{0}}{\pi} \frac{ Ivl }{ Rr }$
  • D
    $\frac{\mu_{0}}{4 \pi} \frac{ Ivl }{ Rr }$

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The figure shows a square loop of side $5 \, cm$ being moved towards the right at a constant speed of $1 \, cm/s$. The front edge enters the $20 \, cm$ wide magnetic field at $t = 0$. Find the magnitude of the $emf$ induced in the loop at $(a) \, t = 2 \, s$, $(b) \, t = 10 \, s$, and $(c) \, t = 22 \, s$.

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$A$ rod of $10 \ cm$ length is moving perpendicular to a uniform magnetic field of intensity $5 \times 10^{-4} \ Wb/m^2$. If the acceleration of the rod is $5 \ m/s^2$, then the rate of increase of induced $emf$ is . . . . . . .

$A$ square-shaped wire loop of mass $m$,resistance $R$,and side $a$ moving with speed $v_{0}$,parallel to the $X$-axis,enters a region of uniform magnetic field $B$,which is perpendicular to the plane of the loop. The speed of the loop changes with distance $x$ $(x < a)$ in the field as:

$A$ jet plane is travelling towards the west at a speed of $1800\, km/h$. What is the voltage difference developed between the ends of the wing having a span of $25\, m$,if the Earth's magnetic field at the location has a magnitude of $5 \times 10^{-4}\, T$ and the dip angle is $30^{\circ}$?

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