Explain with the help of diagrams what spherically and cylindrically symmetric charge distributions are. What is the electric field at a point inside a hollow metallic sphere of radius R having volume charge density p?

A charge distribution is said to be spherically symmetric if the charge density at any point depends only on the distance from the center of the distribution, i.e., the charge density is the same at all points that are equidistant from the center. In a spherically symmetric distribution, the electric field at any point only depends on the radial distance from the center and is directed radially outward or inward.

To understand this better, consider a uniformly charged sphere of radius \( R \) and charge density \( \rho \). The total charge \( Q \) is given by:

\[
Q = \rho \cdot \frac{4}{3} \pi R^3
\]

For this distribution, the electric field at a point outside the sphere, at a distance \( r \) from the center (\( r > R \)), can be determined using Gauss's Law. The symmetry of the charge distribution allows us to consider a spherical Gaussian surface with radius \( r \) ___ _______ _________ ______ ________ ___.
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