Question

The electric field inside a sphere which carries a charge density proportional to the distance from the origin r = µ r (µ is a constant) is:

• A. $\frac{\propto r^{3}}{4\varepsilon_{0}}$
• B. $\frac{\propto r^{2}}{4\varepsilon_{0}}$
• C. $\frac{\propto r^{2}}{3\varepsilon_{0}}$
• D. None of these

Answer 1

Answer: (B)

$\frac{\propto r^{2}}{4\varepsilon_{0}}$

Answer 2

We can consider all the charge inside the sphere to be concentrated at the centre of sphere, consider an elementary shell of radius x and thickness dx

E = $\frac{k\int_{}^{}{dq}}{r^{2}} = \frac{k\int_{0}^{r}{4\pi x^{2}dx( \propto x)}}{r^{2}} = \frac{\propto r^{2}}{4\varepsilon_{0}}$