Electric potential due to an electric dipole

 

Electric potential

due to an electric dipole

 

1) Electric dipole is a combinations of two charges +q and -q, separated by a distance 2a.

2) Dipole moment denoted as P = 2aq and have direction from -q to +q

 

3) Suppose at position A, there is a unit positive test charge.

4) Position A is located r₁ distance from +q charge & r₂ distance from -q charge.

5) From the origin of the dipole O, the position A is a distance of r, making q angle with the dipole.

6) Now potential at A due to +q is

And potential at A due to -q is

7) therefore net potential is

From geometry we know that

 

When r≫a

     

 

Similarly we can find

Now putting the value of  

 

on 2.23 we get      

 

Where P = 2aq  is the dipole moment of the dipole.

1) Potential at equatorial plane, that is 

 

So potential      V(r) = 0

2) Potential o the axis of the dipole,  

So potential is