MCQ
Let there be a spherically symmetric charge distribution with charge density varying as $\text{p}(\text{r})=\text{p}_0\bigg(\frac{5}{4}-\frac{\text{r}}{\text{R}}\bigg)$ upto $r = R$ and $p(r) = 0$ 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.
  • $\text{p}{_0}^\text{r}\Big(\frac{5}{3}-\frac{\text{r}}{\text{R}}\Big)$
  • B
    $\frac{4\pi\text{p}{_0}^\text{r}}{3\in_0}\Big(\frac{5}{3}-\frac{\text{r}}{\text{R}}\Big)$
  • C
    $\frac{4\text{p}{_0}^\text{r}}{4\in_0}\Big(\frac{5}{4}-\frac{\text{r}}{\text{R}}\Big)$
  • D
    $\frac{\text{p}{_0}^\text{r}}{3\in_0}\Big(\frac{5}{4}-\frac{\text{r}}{\text{R}}\Big)$

Answer

Correct option: A.
$\text{p}{_0}^\text{r}\Big(\frac{5}{3}-\frac{\text{r}}{\text{R}}\Big)$

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