Question

If the intensity of electric field at a distance $x$ from the centre in axial position of small electric dipole is equal to the intensity at a distance $y$ in equatorial position, then

• A. $x=y$
• B. $x=y/2$
• C. $y=x/2^{2/3}$
• D. $y=x/2^{1/3}$

Answer 1

The correct option is D $y=x/2^{1/3}$

Electric field due to dipole at axial point

$E_x=\frac{2KP}{x^3}$

Electric field at equilibrial point $E_y=\frac{KP}{y^3}$

$E_x=E_y\Rightarrow \frac{2}{x^3}=\frac{1}{y^3}$

$\Rightarrow y=\frac{x}{2^{1/3}}$