Question

If the magnitude of intensity of electric field at a distance $x$ on axial line and at a distance $y$ on equatorial line for a given dipole are equal, then $x:y$ is $2^{\frac{1}{n}}$. Find the value of $n$.

Answer 1

Magnitude of intensity of the electric field on the axial line of a dipole is $E_{\text{axial}}=\frac{2kp}{r^3}$

Magnitude of intensity of the electric field on the equitorial line of a dipole $E_{\text{equatorial}}=\frac{kp}{r^3}$

Given
$E_{\text{axial}}=E_{\text{equatorial}}\Rightarrow \frac{2kp}{x^3}=\frac{kp}{y^3}$
$\Rightarrow \frac{x}{y}=\frac{2^{1/3}}{1}$

Comparing with the data given in the question we get, $n=3$