Electric Field Intensity on the axial and equatorial line of an electric dipole

Electric Field Intensity at a point on the axial line of an electric dipole

This position is also known as ‘End-on position’.

What is an axial line?
Axial line is the line joining the centres of positive and negative charges forming an electric dipole.

Consider an electric dipole consisting of +q and -q charges separated by a distance 2l.
Consider a point D at a distance ‘r’ from the centre O of the dipole on the axial line of the dipole.

6.png

Let a unit positive charge be placed at point D.

First of all we find electric field at point D due both the charges

  • Electric field intensity at D due to +q charge is given by
daum_equation_1434520425525.png
  • Electric field intensity at D due to -q charge is given by
daum_equation_1434520717441.png

Applying principle of superposition,the net electric field intensity at point D is given by

daum_equation_1434521853172.png
If r >>>>> l
then,
daum_equation_1434522905628.png
Electric Field Intensity at a point on the equatorial line of an electric dipole

This position is also known as ‘Broad-side-on position’.

What is an equatorial line?
The line perpendicular to the axial line and passes through the centre of the electric dipole length is called an equatorial line.

Consi

der an electric dipole AB consisting of +q and -q charges separated by a distance 2l.

Let P be the point on the equatorial line at a distance r from the centre O of the dipole. A unit positive charge is placed at P.

7.png

First of all we find electric field at point P due both the charges

  • Electric field intensity at P due to +q charge is given by
daum_equation_1434523418116.png

  • Electric field intensity at P due to -q charge is given by
daum_equation_1434523373614.png

(E1) and (E2 ) are inclined at an angle of 2θ.Applying parallelogram law of vector addition.As
daum_equation_1434523636972.png
The net electric field intensity(E) due to the electric dipole at point P.
daum_equation_1434524534181.png
If r <<<<< l
then,

daum_equation_1434524835773.png

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