Question

A solid sphere of radius R has a volume charge density $\rho ={\rho }_0{r}^3$ (where ${\rho }_0$ is a constant and r is the distance from center). At a distance x from its centre (for x < R), the electric field is directly proportional to:

• A. $x$
• B. $x^2$
• C. $x^3$
• D. $x^4$

Answer 1

The correct option is D $x^4$

$E=\frac{1}{4\pi {ϵ}_0}\frac{q}{x^2}E=\frac{1}{4\pi {ϵ}_0}\frac{{\int }_0^x{\rho }_0{r}^{3}4\pi r^{2}dr}{x^2}E\propto x^4$