Electric Potential-
Before you go through this article, make sure that you have gone through the previous articles on-
- Electric Field Due To A Charged Thin Spherical Shell
- Relation Between Electric Field & Electric Potential
We have learnt-
The electric field due to a charged thin spherical shell is given by-
The relation between electric field and electric potential is given by-
In this article, we will learn about electric potential due to a charged thin spherical shell.
Electric Potential Due To A Charged Thin Spherical Shell-
Consider a positive charge Q uniformly distributed on the surface of a spherical shell of radius R.
We wish to calculate the electric potential due to a charged thin spherical shell.
There are following three cases possible-
- When observation point lies outside the shell i.e. r > R
- When observation point lies on the surface of shell i.e. r = R
- When observation point lies inside the shell i.e. r < R
Case-01: When observation point lies outside the shell (r>R)
We choose two points-
- The first point say ‘A’ is chosen outside the shell at a distance ‘r’ from the center of shell.
- The second point say ‘B’ is chosen at infinity.
We travel from point A to point B and write the relation between electric field and electric potential.
Using the relation, we have-
Substituting the values we have-
Case-02: When observation point lies on the surface of the shell (r=R)
We choose two points-
- The first point say ‘A’ is chosen on the surface of the shell.
- The second point say ‘B’ is chosen at infinity.
We travel from point A to point B and write the relation between electric field and electric potential.
Using the relation, we have-
Substituting the values we have-
Case-03: When observation point lies inside the shell (r<R)
We choose two points-
- The first point say ‘A’ is chosen inside the shell.
- The second point say ‘B’ is chosen at infinity.
We travel from point A to point B and write the relation between electric field and electric potential.
Using the relation, we have-
Substituting the values we have-
Important NoteIt is interesting to note that the electric potential inside the spherical shell at any point is same as the electric potential on its surface. |
Based on the above discussion, the electric field due to charged thin spherical shell can be summarized as-
Graph-
The following graph shows the variation of electric field intensity due to a charged thin spherical shell with distance from its center-
Read the next article on-
Equipotential Surface & Its Properties
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