$A$ conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure. Two resistors $R_{1}$ and $R_{2}$ are connected across the ends of the rails. There is a uniform magnetic field $\vec{B}$ pointing into the page. An external agent pulls the bar to the left at a constant speed $v$. The correct statement about the directions of induced currents $I_{1}$ and $I_{2}$ flowing through $R_{1}$ and $R_{2}$ respectively is:

  • A
    Both $I_{1}$ and $I_{2}$ are in anticlockwise direction.
  • B
    Both $I_{1}$ and $I_{2}$ are in clockwise direction.
  • C
    $I_{1}$ is in clockwise direction and $I_{2}$ is in anticlockwise direction.
  • D
    $I_{1}$ is in anticlockwise direction and $I_{2}$ is in clockwise direction.

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Suppose a long rectangular loop of width $w$ is moving along the $x$-direction with its left arm in a magnetic field perpendicular to the plane of the loop (see figure). The resistance of the loop is zero and it has an inductance $L$. At time $t=0$,its left arm passes the origin,$O$. If for $t \geq 0$,the current in the loop is $I$ and the distance of its left arm from the origin is $x$,then $I$ versus $x$ graph will be

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When a metal rod of length $l$ is placed in a magnetic field $B$ and moved with velocity $v$ perpendicular to the field,then the induced emf across its ends is

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