Question

A charge Q is distributed uniformly in a sphere (solid). Then the electric field at any point r where r < R (R is radius of the sphere) varies as

• A. $r^{1/2}$
• B. $r^{-1}$
• C. $r$
• D. $r^{-2}$

Answer 1

The correct option is C $r$

If $\rho$ be volume charge density, $Q=\rho .\frac{4}{3}\pi R^3...\left(1\right)$

Consider a Gaussian surface of radius $r$. Using Gauss's law the field at $r$ is

$E.4\pi r^2=\frac{\rho .\frac{4}{3}\pi r^3}{{ϵ}_0}$

$E=\frac{Qr}{4\pi {ϵ}_0{R}^3}$ using (1)

$\therefore E\propto r$