Question

A certain electric dipole consists of charges q and –q separated by distance d, oriented along the x-axis as shown in the figure. find an expression for the magnitude of the electric field e of the dipole at a point far away in the y-direction, a distance r away from the midpoint of the dipole. assume that r is much greater than
d. enter your answer in terms of q, d, r, and ε0.

Answer 1

Electric field due to a point charge is given by formula

$E = \frac{kq}{r^2 + \frac{d^2}{4}}$

now due to negative charge also the magnitude of electric field will be same

only difference is the direction of field due to negative charge is radially inwards

now we can say that net field due to these two charges is given as

$E = 2E_0cos\theta$

$E = 2\frac{kq}{r^2 + \frac{d^2}{4}}*\frac{d/2}{\sqrt{r^2 + \frac{d^2}{4}}}$

$E = \frac{kqd}{(r^2 + \frac{d^2}{4})^1.5}$

now it is given that distance r is very large than "d" so we can say

$E = \frac{kqd}{r^3}$

so above is the electric field due to dipole