$A$ thin disc of radius $b = 2a$ has a concentric hole of radius $a$ in it (see figure). It carries uniform surface charge $\sigma$. If the electric field on its axis at height $h$ $(h << a)$ from its centre is given as $Ch$,then the value of $C$ is:

An electric dipole is placed on the $x$-axis in proximity to a line charge with a linear charge density of $3.0 \times 10^{-6} \, C/m$. The line charge is placed on the $z$-axis. The positive and negative charges of the dipole are at distances of $10 \, mm$ and $12 \, mm$ from the origin,respectively. If a total force of $4 \, N$ is exerted on the dipole,find the magnitude of the positive or negative charge of the dipole.

$A$ cube is placed inside an electric field,$\overrightarrow{E} = 150 y^2 \hat{j}$. The side of the cube is $0.5 \, m$ and it is placed in the field as shown in the figure. The charge inside the cube is $..... \times 10^{-11} \, C$.

According to Gauss's Theorem,the electric field of an infinitely long straight wire is proportional to

$\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is:

If the electric field intensity in a fair weather atmosphere is $100 \, V/m$,then the total charge on the earth's surface is ............ $C$ (radius of the earth is $6400 \, km$).