An electric dipole of dipole moment`vecp` consists of point charges +q and −q separated by a distance 2a apart. Deduce the expression for the electric field `vecE` due to the dipole at a distance x from the centre of the dipole on its axial line in terms of the dipole moment `vecp`. Hence show that in the limit x>> a, `vecE->2vecp"/"(4piepsilon_0x^3)`
Electric Field on Axial Line of an Electric Dipole
Let P be at distance r from the centre of the dipole on the side of charge −q. Then, the electric field at point P due to charge −q of the dipole is given by
Where `hatp `is the unit vector along the dipole axis (from − q to q).
Also, the electric field at point P due to charge +q of the dipole is given by
The total field at P is
r = x
For x >> a,