Question

Let there be a spherically symmetric charge distribution with charge density varying as ρ(r) = ρ₀ (5/4 - r/R) upto r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r (r < R) from the origin is given by

Answer 1

(c) : Consider a thin spherical shell of radius x and thickness dx as shown in the figure.

Volume of the shell, dV = 4πx²dx
Let us draw a Gaussian surface of radius r(r < R) as shown in the figure above.
Total charge enclosed inside the Gaussian surface is