Electric Field Intensity at any point due to an Ideal Dipole

What is an Electric Field Intensity?

The space around an electric charge in which its influence can be felt is known as the electric field. At a point, the electric field intensity is the force experienced by a unit positive charge placed at that point. The electric field intensity due to a positive charge is always directed away from the charge and the intensity due to a negative charge is always directed towards the charge. Electric Field Intensity is a vector quantity.

Read More: Electric Field Intensity

What is an Electric Dipole?

An electric dipole is defined as a pair of opposite charges q and –q separated by a distance d.

Electric Field Intensity of an Electric Dipole Derivation

Derivation of Electric Field Intensity for points on the Axial Line of a Dipole

Electric Field Intensity of an Electric Dipole Derivation

Consider a system of charges -q and +q separated by a distance 2a. Let “P” be any point on the axial line where the electric field intensity needs to be determined.

Electric Field at P (EB) due to +q is given as follows:



\(E_{B}=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{BP^2}\)



\(E_{B}=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{(r-a)^2}\)



The electric field at P (EA) due to -q is given as follows:



\(E_{A}=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{(AP)^2}\)



\(E_{A}=\frac{1}{4\pi \varepsilon _{0}}\frac{q}{(r+a)^2}\)



The following equation gives the net field at point P:



\(E_{P}=E_{B}-E_{A}\)



\(=\frac{1}{4\pi \epsilon _{0}}\frac{q}{(r-a)^2}-\frac{q}{(r+a)^2}\)



Simplifying the above equation, we get



\(E_{p}=\frac{q}{4\pi \epsilon _{0}}\times \frac{2r}{(r^2-a^2)^2}\)



Further simplifying, we get



\(E_{p}=\frac{2kpr}{(r^2-a^2)^2}\)



In the equation, p = 2aq and \(k = \frac{1}{4\pi \epsilon _{0}}\)


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