Question

Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the center?

• A.
• B.
• C.
• D.

Hint:

The electric potential inside a spherical conductor is uniform and equal to the surface potential. Outside, the potential decreases with distance from the center.

Answer 1

The Correct Option is D

To understand the variation of electric potential \( V \) with the radial distance \( r \) from the center of a charged spherical conductor, we need to explore the electric potential behavior both inside and outside the conductor:

1. Inside the Conductor \((r \leq R)\):
   • The electric potential inside a charged conductor is constant. This is because the electric field inside is zero, and no work is required to move a charge inside the conductor.
   • Therefore, the potential \( V \) at a distance \( r \leq R \) is equal to the potential at the surface, \( V = \frac{KQ}{R} \), where \( K \) is the Coulomb's constant and \( Q \) is the total charge on the conductor.
2. Outside the Conductor \((r > R)\):
   • For points outside the charged spherical conductor, it behaves like a point charge located at its center.
   • The electric potential \( V \) at a distance \( r \) from the center is given by \( V = \frac{KQ}{r} \).
   • This implies that the potential decreases inversely with distance \( r \). 

Based on this understanding, the graph representing the variation of electric potential with radial distance \( r \) from the center should be constant (horizontal line) for \( r \leq R \) and then decrease inversely with \( r \) for \( r > R \). The correct graph option representing this behavior is:

Thus, the graph correctly depicts a constant potential inside the conductor and a decreasing potential outside, following the inverse relation with distance.