Electric Charges and Fields

The nuclear charge $$(Ze)$$ is non-uniformly distributed within a nucleus of radius $$R$$. The charge density $$ \rho \left( r \right)$$ [charge per unit volume] is dependent only on the radial distance $$r$$ from the center of the nucleus as shown in figure The electric field is only along the radial direction.
When we remove polyester or woolen cloth in dark, we can see a spark and hear a cracking sound. These are due to:
If the dielectric constant is K then,  find the electric field at equator of dipole?
The Gravitational force between two point masses separated by a distance $$r$$ is proportional to $$\dfrac{1}{r^2}$$, just like the electric force between two point charges. Because of this similarity between gravitatonal and electrical interactions, there is also a Gauss's law for gravitation. Let $$g$$ be the acceleration due to gravity caused by point mass $$m$$ at the origin so that $$g = \dfrac{-Gm}{r^2} \hat{r}$$. Consider a spherical Gaussian surface with radius $$r$$ centered on this point mass. 
A thin, rigid insulated rod of mass m and length $$l$$ carrying a charge Q uniformly distributed along its length is smoothly pivoted at P. It is placed in between the charged large conducting plates. Disregard gravity.