The net electric field at point $P$ due to the segments $dq_1$ and $dq_2$ of a uniformly charged spherical shell is ...... ($C$ is the center of the shell.)

Let $\rho (r) = \frac{Q}{\pi R^4} r$ be the volume charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $p$ inside the sphere at distance $r_1$ from the centre of the sphere,the magnitude of the electric field is:

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+\sigma$ and $-2 \sigma$. The force experienced by a point charge $+q$ placed at the midpoint between the two plates will be:

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 $6400 \, km$).

An infinite non-conducting sheet has a surface charge density $2 \times 10^{-7} \text{ C/m}^2$ on one side. The distance between two equipotential surfaces whose potential difference is $90 \text{ V}$ is (assume $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2$):

The volume charge density of a sphere of radius $6 \, m$ is $2 \, \mu C \, m^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is $.... \times 10^{10} \, N C^{-1}$. [Given: Permittivity of vacuum $\epsilon_{0} = 8.85 \times 10^{-12} \, C^{2} N^{-1} m^{-2}$]