Equipotential surface and its properties

“Equipotential surface”:
The Equipotential surface is the imaginary surface in an electric field on which the value of electric potential is same at all the points of it.  The shape of equipotential surface are different in different electric field.

*“ properties”:

1) The potential at every point on equipotential surface remain same.

2) On the equipotential surface no work is done in bringing a charge.

3) The electric field lines are always normal to the equipotential surface.

4) Two equipotential surface can never intersect Each Other because if two equipotential surfaces intersect at a point than two different value of potential are obtained at one point which is not possible.

5) The surface of conductor is always equipotential surface.


2nd topic :

*) Electric field intensity inside the charged spherical conductor is zero but a potential is constant, why ?

 when some amount of charge is given to the sperical conductor this total charge uniformly distributed on its outer surface. There is no charge resides inside the conductor i.e  Q = 0 . Thus electric field intensity, E = 0.

We know that potential difference , ΔV = E × Δx

Put  E = 0

ΔV = 0 × Δx
ΔV = 0
i.e  V = constant

It is clear that inside the charged conducting sphere electric potential is same at each point And this is equal to the potential produce on its surface.

According to the diagram the electric field lines of the charged spherical conductor are radial that is they appear to coming from the centre. Thus we can assume that the total charges resides on the surface is to be concentrated at its Centre And this charge behaves like point charge

Thus the electric potential due to point charge +Q (imaginary charge concentrated at centre) at the distance ‘R’ (at the surface of a sphere) is ---

          V = 1/4π£o × Q/R       volt