Question

Choose correct graph of electric potential for uniformly charged hollow sphere. 

• A.
• B.
• C.
• D.

Answer 1

The Correct Option is D

To determine the graph of electric potential for a uniformly charged hollow sphere, we need to understand how the potential varies with distance from the center of the sphere.

For a uniformly charged hollow sphere:

1. Outside the Sphere (r > R): The electric potential \(V\) at a distance \(r\) outside the sphere is given by: \(V = \frac{KQ}{r}\), where \(K\) is the Coulomb's constant and \(Q\) is the total charge of the sphere. The potential decreases with increasing \(r\).
2. On the Surface of the Sphere (r = R): The potential remains constant and is equal to: \(V = \frac{KQ}{R}\).
3. Inside the Sphere (r < R): The electric field inside a hollow sphere is zero due to the uniform distribution of charge. Thus, the potential remains constant and equal to the potential at the surface, \(V = \frac{KQ}{R}\).

The graph that correctly represents this behavior is a graph where:

• The potential is constant inside the sphere and up to the surface of the sphere.
• The potential decreases inversely proportional to \(r\) outside the sphere.

Thus, the correct graph is the one that shows a flat line from \(r = 0\) up to \(r = R\) (constant potential), and decreases inversely with \(r\) beyond \(r = R\). This matches the description of the image option:

This concludes that the correct graph for the electric potential of a uniformly charged hollow sphere is depicted in the above image.