Question

Obtain an expression for the electric field along the axial lineof an electric dipole

Answer 1

Answer:

To find electric field at point P on the axial line of the dipole, OP=r. Let E1 and E2 be electric field on P due to charges +q and −q respectively. If r>>a, then E=kr42pr=kr32p. In vector form, E =kr32p

Answer 2

Consider the an electric dipole of charges +q and −q separated by distance 2a with center at O. 

Goal: To find electric field at point P on the axial line of the dipole, OP=r. 

Let E1 and E2 be electric field on P due to charges +q and −q respectively. 

E1=(r−a)2kq along AP 

E2=(r+a)2kq along BP

The resultant electric field at P, E=E1−E2 (as both E1 and E2 are in opposite direction) 

E=(r−a)2kq−(r+a)2kq=kq(r2−a2)24ra

Define,  p=2aq 

E=k(r2−a2)22pr

If r>>a, then E=kr4