Q.

Derive an expression for the intensity of the electric field at a point on the axial line of an electric dipole.

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Detailed Solution

Consider an electric dipole consisting charges –q and q, seperated by a distance 2a. Let p be a point on the axial line of a dipole at a distance r from centre of dipole as shown in figure
Electric field due to charge –q at P is

Eq=14πϵ0q(r+a)2 towards left 
Electric field due to charge +q at P is
E+q=14π0q(ra)2 towards right 
Resultant electric field at point P is
Eaxial=14π0q(ra)214π0q(r+a)2Eaxial=q4π01(ra)21(r+a)2
Eaxial=q4π0(r+a)2(ra)2(ra)2(r+a)2Eaxial =q4π04rar2a22Eaxial =q4π02(2a)(q).rr2a22Eaxial=24πϵ0Prr2a22
if a<<<r then 'a' is negligible
Eaxial =24πϵ0Prr4Eaxial =14πϵ02Pr3
The direction of E is in the direction of dipole moment

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