The problem requires us to determine the correct graph for the electric potential \(V\) as a function of the distance \(r\) from the center of a uniformly charged spherical shell with radius \(R\).
Concept:
A uniformly charged spherical shell has the following properties related to electric potential:
Inside the shell \((r < R)\): The electric potential \(V\) is constant and equal to the potential at the surface.
On the surface or outside the shell \((r \geq R)\): The potential decreases with distance according to the formula for a point charge, \(V = \frac{kQ}{r}\), where \(k\) is the Coulomb's constant and \(Q\) is the total charge.
Explanation:
The potential graph should show a constant value from the center to the surface \((r = R)\), and then start decreasing as \(r\) increases beyond the surface.
Correct Graph:
This graph shows that the potential is constant within the shell \((r < R)\) and decreases for \(r \geq R\), which matches the theoretical behavior of a uniformly charged spherical shell.
Conclusion:
The correct graph for the electric potential \(V\) as a function of distance \(r\) from the center of the charged spherical shell is option 4.
