Question

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

Answer 1

Solution:

The electric potential \( V \) due to a uniformly charged hollow sphere is given by the following properties: 

1. Inside the hollow sphere (r < R):
The electric potential is constant and the same as at the surface of the sphere. This is because the electric field inside a uniformly charged spherical shell is zero. Thus, the potential is not dependent on the distance inside the sphere but remains constant. 
2. At the surface of the sphere (r = R):
The electric potential is equal to the potential at the surface, which can be found using the formula for the potential due to a uniformly charged sphere: 
\[ V = \frac{kQ}{R} \] where \( k \) is Coulomb’s constant, \( Q \) is the total charge on the sphere, and \( R \) is the radius of the sphere. 
3. Outside the hollow sphere (r > R):
The electric potential behaves like that of a point charge and decreases with distance as \( \frac{1}{r} \). The potential outside the sphere is: 
\[ V = \frac{kQ}{r} \] 

Correct Graph:
The graph should show that the electric potential is constant inside the sphere, equal to the potential at the surface, and then decreases with \( 1/r \) for \( r > R \). Based on this, the correct graph is option 4.