As shown in the figure, a point charge $q_{1} = +1 \times 10^{-8} \ C$ is placed at the origin in the $x-y$ plane and another point charge $q_{2} = +3 \times 10^{-6} \ C$ is placed at the coordinate $(10, 0)$. In that case, which of the following graph$(s)$ shows most correctly the electric field vector $E_{x}$ in the $x$-direction?

How much work is done in moving a charge $+q$ once around a circle of radius $r$ in the presence of a central charge $+Q$?

For two electrons separated by a distance of $10 \, cm$,let $F_g$ and $F_e$ represent the gravitational force and electrostatic force between them,respectively. The ratio $F_g / F_e$ is of the order of:

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 $z_0 < R$.

Which of the field patterns given below is valid for electric field as well as for magnetic field?

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s \text{ C/m}^2$ is placed on the $x-y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \text{ C/m}$ is placed at the $z=4 \text{ m}$ plane and is parallel to the $y$-axis. If the magnitude values satisfy $|\sigma_s| = 2|\lambda_e|$,then at the point $(0, 0, 2)$,the ratio of the magnitudes of the electric field values due to the sheet charge to that of the line charge is $\pi \sqrt{n} : 1$. The value of $n$ is: