The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance from its center is represented by which of the following graphs?

Which of the following patterns of electric field lines is $NOT$ possible for an electrostatic field due to static charges?

Two small spheres of each charge $q$,mass $m$ and material density $d$ are suspended from a fixed point with the help of inextensible light threads. When the spheres are in air,the angle between the threads is $90^{\circ}$. When the spheres are suspended in a liquid of density $\frac{2}{3} d$,the angle between the threads is $60^{\circ}$. The value of the dielectric constant of the liquid is

Consider a uniformly charged hemispherical shell of radius $R$ and charge $Q$. If the electric field at point $A (0, 0, -z_0)$ is $\vec E$,then find the electric field at point $B (0, 0, z_0)$,where $z_0 < R$.

$A$ charged cork of mass $m$ suspended by a light string is placed in a uniform electric field of strength $E = (\hat{i} + \hat{j}) \times 10^5 \ NC^{-1}$ as shown in the figure. If in the equilibrium position,the tension in the string is $\frac{2mg}{(1 + \sqrt{3})}$,then the angle $\alpha$ with the vertical is:

For the given figure,the direction of the electric field at point $A$ will be .........