Two long conductors are arranged as shown above to form overlapping cylinders, each of radius $r$, whose centres are seprated by a distance $d$. Current of density $\mathrm{J}$ flows into the plane of the page along the shaded part along the shaded portion of the other, as shown. What are the magnitude and direction of the magnetic field at point $A$?

$OABC$ is a current carrying square loop. An electron is projected from the centre of loop along its diagonal $AC$ as shown. Unit vector in the direction of initial acceleration will be

An electron moving with a velocity $\overrightarrow{{\mathrm{v}}_1}=2\hat{\mathrm{i}} \mathrm{m} {\mathrm{s}}^{-1}$  at a point in a magnetic field experiences a force $\overrightarrow{{\mathrm{F}}_1}=-2\hat{\mathrm{j}} \mathrm{N}.$ If the electron is moving with a velocity $\overrightarrow{{\mathrm{v}}_2}=2\hat{\mathrm{j}} \mathrm{m} {\mathrm{s}}^{-1}$ at the same point, it experiences a force $\overrightarrow{{\mathrm{F}}_2}=2\hat{\mathrm{i}} \mathrm{N}$. The force electron would experience if it were moving with a velocity $\overrightarrow{{\mathrm{v}}_3}=2\hat{\mathrm{k}} \mathrm{m} {\mathrm{s}}^{-1}$  at the same point is  

In the figure shown a coil of single turn is would on a sphere of radius $R$ and mass $m$. The plane of the coil is parallel to the plane and lies in the equatorial plane of the sphere. Current in the coil is $i$. The value of $B$ if the sphere is in equilibrium is

A thin non-conducting disc of radius $R$ is rotating clockwise (see figure) with an angular velocity $\omega$ about its central axis, which is perpendicular to its plane. Both its surface carry $+\mathrm{ve}$ charges of uniform surface density. Half the disc is in region of a uniform, unidirectional magnetic field $B$ parallel to the disc, as shown. Then,