A conducting rod $AC$ of length $4l$ is rotated about a point $O$ in a uniform magnetic field $\overrightarrow{B}$, directed into the paper. $AO=l$ and $OC=3l$. Then:

A simple pendulum with a bob of mass $m$ and conducting wire of length $L$ swings under gravity through an angle $2\mathrm{\theta }$. The earth's magnetic field component in the direction perpendicular to swing is $B$. Maximum potential difference induced across the pendulum is:

A square metallic wire loop of side $0.1 \mathrm{m}$ and resistance of $1 \mathrm{\Omega }$ moves with a constant velocity in a magnetic field of $2 \mathrm{Wb} {\mathrm{m}}^{-2}$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop which is connected to a network of resistances. What should be the velocity of loop so as to have a steady current of $1 \mathrm{mA}$ in the loop?

A conducting rod $PQ$ of length $L=1.0 \mathrm{m}$ is moving with a uniform speed $v=2 \mathrm{m} {\mathrm{s}}^{-1}$ in a uniform magnetic field $B=4.0 \mathrm{T}$, directed into the paper. A capacitor of capacity $C=10 \mu \mathrm{F}$ is now connected to the rod, as shown in the figure. Then:

​​​​​​​

A rectangular loop, with a sliding connector of length $l=1.0 \mathrm{m}$, is situated in a uniform magnetic field $B=2 \mathrm{T}$, perpendicular to the plane of loop. Resistance of the connector is, $r=2 \mathrm{\Omega }.$ Two resistances of $6 \mathrm{\Omega }$ and $3 \mathrm{\Omega }$ are connected, as shown in the figure. The external force required to keep the connector moving with a constant velocity $v=2 \mathrm{m} {\mathrm{s}}^{-1}$ is:

A pair of parallel conducting rails lie at right angle to a uniform magnetic field of $2.0 \mathrm{T}$, as shown in the figure. Two resistors of $10 \mathrm{\Omega }$ and $5 \mathrm{\Omega }$ are to slide, without friction, along the rail. The distance between the conducting rails is $0.1 \mathrm{m}$. Then:

The magnetic field within a cylindrical region, whose cross-section is as indicated, starts increasing at a constant rate of $\alpha \mathrm{T} {\mathrm{s}}^{-1}$. The graph showing the variation of induced field with distance $r$ from the axis of cylinder is:

A square non-conducting loop, $20 \mathrm{cm}$ on a side, is placed in a magnetic field. The centre of side $AB$ coincides with the centre of magnetic field. The magnetic field is increasing at the rate of $2 \mathrm{T} {\mathrm{s}}^{-1}$. The potential difference between $B$ and $C$ is:

A square non-conducting loop, $20 \mathrm{cm}$ on a side, is placed in a magnetic field. The centre of side $AB$ coincides with the centre of magnetic field. The magnetic field is increasing at the rate of $2 \mathrm{T} {\mathrm{s}}^{-1}$. The potential difference between $C$ and $D$ is: