Potential due to Elelctric Dipole

Assume there is a fight going on in your house.

The fight will not only affect your family but also disturb the peace of your neighbours.

Similarly, presence of a dipole will affect its neighbouring region.

Let us see what effect a dipole causes at any neighbouring point.

Consider a dipole AB with charges of magnitude ‘q’ and length ‘2l’ .

Assume a point P is at a distance ‘r’ at some angle from the centre ’O’ of a dipole.

Let ‘r1‘ and ‘r2’ be the distances between point ‘P’ and point charges.

Let potential at point ‘p’ due to point charges be ‘V1’ and ‘V2’

Now, drop a perpendicular from A and B on the line OP.

So, from the figure PB’ and PA’ are :

Consider the right angled triangles OBB’ and OAA’ .

Thus, the value of PA’ and PB’ become:

As the length of dipole is small i.e. l<<

So, on putting the values of r1 and r2 , V1 and V2 become:

Now,the total potential V at point P becomes :

We know that l<<

We know that , p=2ql. So, V becomes:

Let us find the potential at point P for some orientations.

Case 1:Point P is perpendicular to axis i.e. lies on equator of dipole:

Case 2:Point P is along the axis of dipole ,near negative charge:

Case 3:Point P is along the axis of dipole, near positive charge:

Let’s revise what we have studied.

The potential at a point P due to a dipole is given by:

Potential at point P at some specific angles :

Keep Swiping :)