Question

A sphere of radius $R$ has a charge density which varies with distance as $\rho =A\sqrt{r}$. The electric field at a distance $r<R$ varies with $r$ as

• A. $E\propto r^{-1/2}$
• B. $E\propto r^{1/2}$
• C. $E\propto r^{3/2}$
• D. $E\propto r^{-2}$

Answer 1

The correct option is B $E\propto r^{1/2}$

Radius $=R$

distance as $P=A\sqrt{r}$

electric field at a distance $r<R$ varies with $r$.

From the formula, we get,

$E=\frac{1}{4\pi {ϵ}_0}\frac{q}{r^2}$

$E$ $\alpha$ $\frac{1}{r^2}$

or, $E$ $\alpha$ $r^{-2}$

but in this situation we get,

$E$ $\alpha$ $r^{1/2}$

($\because$ $P=A{r}^{1/2}$)