Deutron and $\alpha - $ particle are put $1\,\mathop A\limits^o $ apart in air. Magnitude of intensity of electric field due to deutron at $\alpha - $ particle is

The number of electrons to be put on a spherical conductor of radius $0.1\,m$ to produce an electric field of $0.036\, N/C$ just above its surface is

Two identical non-conducting solid spheres of same mass and charge are suspended in air from a common point by two non-conducting, massless strings of same length. At equilibrium, the angle between the strings is $\alpha$. The spheres are now immersed in a dielectric liquid of density $800 kg m ^{-3}$ and dielectric constant $21$ . If the angle between the strings remains the same after the immersion, then

$(A)$ electric force between the spheres remains unchanged

$(B)$ electric force between the spheres reduces

$(C)$ mass density of the spheres is $840 kg m ^{-3}$

$(D)$ the tension in the strings holding the spheres remains unchanged

A thin conducting ring of radius $R$ is given a charge $+Q.$ The electric field at the centre $O$ of the ring due to the charge on the part $AKB$ of the ring is $E.$ The electric field at the centre due to the charge on the part $ACDB$ of the ring is 

Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q.$ The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2} L$.

The electric field in a region is radially outward and at a point is given by $E=250 \,r V / m$ (where $r$ is the distance of the point from origin). Calculate the charge contained in a sphere of radius $20 \,cm$ centred at the origin ......... $C$