Question

what is the value of |Eax/Eeq| for a short electric dipole​

Answer 1

Given:

A short electric dipole has been provided.

To find:

Ratio of electrostatic field intensity at the axial position to the equatorial position.

$\boxed{ \sf{ \dfrac{E_{ax}}{E_{eq}} = \: ?}}$

Calculation:

Since , we have assumed a short electric dipole, we can consider the inter-charge distance to be much smaller as compared to the equatorial or axial position.

$\boxed{ \sf{2a \: < < \: x}}$

At the axial position , the Electrostatic Field Intensity will be :

$\therefore \: E_{ax} = \dfrac{2kp}{ {r}^{3} }$

At equatorial position , the Electrostatic Field Intensity is :

$\therefore \: E_{eq} = \dfrac{kp}{ {r}^{3} }$

Hence the ratio will be :

$\therefore \: \dfrac{E_{ax}}{E_{eq}} = \dfrac{ (\dfrac{2kp}{ {r}^{3} }) }{ (\dfrac{kp}{ {r}^{3} } )} = 2$

$= > \: E_{ax} : E_{eq} = 2 : 1$

So , final answer is :

$\boxed{ \large{ \sf{ E_{ax} : E_{eq} = 2 : 1}}}$