Question

Derive electric field by a dipole on its axial line and also equatorial line?​

Answer 1

Answer:

Electric field due to an electric dipole at a point on its axial line: AB is an electric dipole of two point charges −q and +q separated by small distance 2d. P is a point along the axial line of the dipole at a distance r from the midpoint O of the electric dipole.

The electric fiedl at the point P due to +q placed at B is,

E1=4πε01(r−d)2q (along BP)

The electric field at the point P due to −q placed at A is,

E2=4πε01(r+d)2q (along PA)

Therefore, the magnitude of resultant electric field (E) acts in the direction of the vector with a greater, magnitude. The resultant electric field at P is

E=E1+(−E2)

E=[4πε01(r−d)2q−4πε01(r+d)2q] along BP

E=4πε0