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 :)