A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment $\mathrm{p}$. If the…

A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment $\mathrm{p}$. If the distance of $\mathrm{Q}$ from the dipole is $\mathbf{r}$ (much larger than the size of the dipole), then the electric field at $\mathrm{Q}$ is proportional to
  1. $\mathrm{p}^{-1}$ and $\mathrm{r}^{-2}$
  2. $\mathrm{p}$ and $\mathrm{r}^{-2}$
  3. $\mathrm{p}^{2}$ and $\mathrm{r}^{-3}$
  4. $\mathrm{p}$ and $\mathrm{r}^{-3}$

Solution

$\mathrm{E}=\frac{\mathrm{p}}{4 \pi \varepsilon_{0} \cdot \mathrm{r}^{3}}$
Apparently, $\mathrm{E} \propto \mathrm{p}$ and $\mathrm{E} \propto \frac{1}{\mathrm{r}^{3}} \propto \mathrm{r}^{-3}$.

Asked in: JEE Mains - Electrostatics - Test 5

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