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

• A. $1:1$
• B. $1:\sqrt{2}$
• C. $1:2$
• D. $2^{1/3}:1$

Answer 1

The correct option is D $2^{1/3}:1$

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