Equipotential Surface : Why Is The Electric Potential Same Everywhere Inside A Conductor
Electric potential of a point is the work done by electric force to bring a 1 coulomb positive charge from infinity to the point. Suppose, the potential of point A near the charge q is 5 volt. This means if you bring a 1 coulomb positive charge from infinity to point A, you have to do 5 J work against the repulsive force of the charge q. Because, both charge will repel each other.
As electric force is a conservative force, the work doesn’t depend on which path you choose to bring the charge from infinity to point A. This is the same work the electric force will do if you left the charge at A point. Then the repulsive coulomb’s force will push the 1 coulomb’s charge to infinity and it will do exactly 5 J work to do this. The potential difference between two points is the difference between their potential. Let another point B has a potential of 8 volt.
So, the potential difference between A and B is 8–5=3 volt. This potential difference means that to bring a 1 coulomb charge from A to B, you need to do 3 J of work. You can read this article on Electric Potential & Electric Potential Energy if you want to learn more about potential :
If there is no electric field in a place, then there will be no electric force on any charge. And so, the potential difference between any two point will be zero. Because, work = force * distance. If there is no force, there will be no work. So, you need not do any work to move a charge between any two point.
Thus, their potential difference will be zero and both of the point will have same potential.
This to points are equipotential points as both of them have same potential. A surface is called equipotential if every point on the surface has same potential. For example, consider a charge q at the center of a sphere with radius r.
Each point above the surface of the sphere is located at a distance of r from the center. So, the electric potential V is same for every point on the sphere. Because electric potential depends only on the distance from the charge. So the surface of the sphere is an equipotential surface.
Electric Potential Inside A Conductor
The net electric field inside a conductor is always zero. So, there is no electric field lines inside a conductor.In conductor , electrons of the outermost shells of the atoms can move freely through the conductor. These electrons are called free electrons.
Now, let an external electric field E is applied on the conductor. So, there will be some electric field line inside the conductor.
If a charge q is put inside an electric field, an electric force F will be applied on it .
F = q*E
If the charge is negative, the direction of the electric force will be opposite to the direction of the electric field E. So, if an external electric field E is applied on a conductor, each free electron will feel an electric force F opposite to the direction of E.
As the free electrons can move freely inside the conductor, the electrons will move to the left side of the conductor . Thus , there will be a net negative charge on the left side and a net positive charge on the right side.
These net negative and positive charges are called induced charge. This induced charge will create an electric field inside the conductor. This electric field is called induced electric field. In the following figure, only induced charges are shown.
The new induced electric field Eᵢ and the external electric field E are opposite in direction. So, the net electric field inside the insulator is ,
E’ = E — Eᵢ …………(1)
As long as the magnitude of Eᵢ is smaller than E, electron will keep moving to the left and more positive and negative charge will be formed on both right and left side. So, Eᵢ will become stronger. When Eᵢ = E, then the net electric field inside the conductor = E — Eᵢ = 0.
So, eventually the net electric field inside the conductor will be zero and there will be some negative charge on the left surface and some positive charge on the right surface.
As the electric field inside the conductor is zero, all the points inside the conductor including the points on the surface will have same potential. In other words they are all equipotential points.
