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 â€˜qâ€™ and length â€˜2lâ€™ .
Assume a point P is at a distance â€˜râ€™ at some angle from the centre â€™Oâ€™ of a dipole.
Let â€˜r1â€˜ and â€˜r2â€™ be the distances between point â€˜Pâ€™ and point charges.
Let potential at point â€˜pâ€™ due to point charges be â€˜V1â€™ and â€˜V2â€™
Now, drop a perpendicular from A and B on the line OP.
So, from the figure PBâ€™ and PAâ€™ are :
Consider the right angled triangles OBBâ€™ and OAAâ€™ .
Thus, the value of PAâ€™ and PBâ€™ 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:
Letâ€™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 :)