Q.(a) Derive an expression for electric field intensity due to an electric dipole at a point on its axial line. OR

An electric dipole consists of two equal and opposite charges +q and -q separated by a small distance 2a; its strength and orientation are captured by the dipole moment vector p = q(2a), directed by convention from the negative charge toward the positive charge. The dipole's own field, found by superposing the two individual point-charge fields, works out differently along two special directions. On the axial line (through both charges, extended), for a field point far away (distance r much greater than a), the field is E_axial is approximately 2kp/r^3, directed parallel to p. On the equatorial line (the perpendicular bisector plane through the dipole's midpoint), the field is E_equatorial is approximately kp/r^3 -- exactly half the axial value at the same distance -- d …