If the magnitude of intensity of electric field at a distance ' $\mathrm{r}_1$ ' on an axial line and at a…

If the magnitude of intensity of electric field at a distance ' $\mathrm{r}_1$ ' on an axial line and at a distance ' $r_2$ ' on an equatorial line due to a given short dipole are equal, then $r_1: r_2$, is
  1. $\sqrt[3]{2}: 1$
  2. $\sqrt{2}: 1$
  3. $1: 2$
  4. $1: \sqrt[3]{2}$

Solution

$\begin{aligned} & E_{\text {axial }}=E_{\text {equatorial }} \Rightarrow k \frac{2 p}{r_1^3}=\frac{k p}{r_2^3} \\ & \Rightarrow \frac{r_1}{r_2}=\frac{2^{1 / 3}}{1}=\sqrt[3]{2}: 1\end{aligned}$

Asked in: MHT CET 2023 (13 May Shift 1)

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