If electric field in a region is radially outward with magnitude $\mathrm{E}=\mathrm{Ar}$, the charge…

If electric field in a region is radially outward with magnitude $\mathrm{E}=\mathrm{Ar}$, the charge contained in a sphere of radius $\mathrm{r}$ centred at the origin is
  1. $\frac{1}{4 \pi \varepsilon_{\mathrm{o}}} \mathrm{Ar}^{3}$
  2. $4 \pi \varepsilon_{0} \mathrm{Ar}^{3}$
  3. $\frac{1}{4 \pi \varepsilon_{0}} \frac{A}{r^{3}}$
  4. $\frac{4 \pi \varepsilon_{0} \mathrm{~A}}{\mathrm{r}^{3}}$

Solution

$\mathrm{E}=\frac{\mathrm{q}}{4 \pi \varepsilon_{\mathrm{o}} \mathrm{r}^{2}} \Rightarrow \mathrm{Ar}=\frac{\mathrm{q}}{4 \pi \in_{0} \mathrm{r}^{2}}$
$\Rightarrow \mathrm{q}=4 \pi \varepsilon_{\mathrm{o}} \mathrm{Ar}^{3}$ .

Asked in: JEE Mains - Electrostatics - Test 2

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