Equipotential surface


1) Equipotential surface is a surface where the potential at any point on the surface is same or constant.

2) Suppose a charge q is in space, the potential at a distance r from the surface is


3) This potential is always constant at a distance r from the charge, So equipotential surface for the charge q is a spherical surface.


4) Electric field is normal to the equipotential surface




Here equipotential surface is

normal to the electric field.

 

 

  

 

Relation between electric

field & Potential

 

1) Suppose there are two equipotential surface A & B.

2) A surface has potential V+dV

3) B Surface has V potential. As shown below.

 


 

4) dV is the potential decreases when you move along the electric field E from A to B.


5) Now work done on brining a unit positive test charge Against the electric field from the surface B to surface A is

W = - E.dr


6) this work done is equal to the potential difference between the two surfaces A & surface B.


W = VA – VB = (V+dV) - V

W = dV


7) Now we got that

W = - E.dr = dV

Therefore



8) The  negative sign tells that electric field decreases in the direction same as the potential also decreases.