To determine the correct graph for the electric potential V radially away from the center of a uniformly charged thin spherical shell, we need to understand the behavior of electric potential in this scenario.
Concept and Explanation:
For a uniformly charged thin spherical shell, the electric potential V at a distance r from the center is defined by the following conditions:
Outside the shell (r > R), the electric potential V behaves as if the entire charge were concentrated at the center. The formula is:
V = \frac{kQ}{r}, where k is Coulomb's constant and Q is the total charge.
On the shell (r = R), the potential is constant:
V = \frac{kQ}{R}.
Inside the shell (r < R), the potential remains constant and equal to the potential on the surface:
V = \frac{kQ}{R}.
Therefore, the graph of V as a function of r should show these characteristics:
Constant for r \leq R.
Decreasing as \frac{1}{r} once r > R.
The correct graphical representation is the fourth option:
