Question

Electric field on the axis of a small electric dipole at a distance r is E1 and E2 at a distance of 2r, on a line of perpendicular bisector. Then, (E1 / E2) is a) 2 b) 4 c) 8 d) 16​

Answer 1

Given:

Electric field on the axis of a small electric dipole at a distance r is E1 and E2 at a distance of 2r.

To find:

Ratio of E1 and E2 ?

Calculation:

• For any small dipole, the electric field intensity on equatorial line is proportional to 1/d³.

• $\boxed{\bf E \propto \dfrac{1}{d^{3}}}$

So, when d is r and 2r respectively, the required ratio is :

$\implies \dfrac{ E_{1}}{E_{2} } = \dfrac{ {(2r)}^{3} }{ {r}^{3} }$

$\implies \dfrac{ E_{1}}{E_{2} } = \dfrac{ 8{r}^{3} }{ {r}^{3} }$

$\implies \dfrac{ E_{1}}{E_{2} } = 8$

So, the required ratio is 8 .