For a spherical shell

Options

A. If potential inside it is zero then it necessarily electrically neutral
B. Electric field in a charged conducting spherical shell can be zero only when the charge is uniformly distributed.
C. Electric potential due to induced charges at a point inside it will always by zero
D. None of these

Answer

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to analyze the electric field and electric potential inside a spherical shell with charge distributed on its surface.

2. **Electric Field Inside the Shell**: According to Gauss's Law, the electric field inside a uniformly charged spherical shell is zero. This is because the symmetry of the shell causes the electric field contributions from all parts of the shell to cancel out at any point inside.

\[ E_{\text{inside}} = 0 \]

3. **Electric Potential Inside the Shell**: The electric potential at any point inside the shell can be derived from the electric field. Since the electric field inside the shell is zero, the potential remains constant throughout the interior of the shell.

4. **Calculating the Potential**: The potential \( V \) at a point inside the shell can be calculated using the formula for the potential due to a point charge. However, since the electric field is zero inside the shell, the potential is equal to the potential at the surface of the shell.

\[ V_{\text{inside}} = V_{\text{surface}} \]

5. **Potential at the Surface**: The potential at the surface of a charged spherical shell can be calculated using the formula:

\[ V = \frac{1}{4 \pi \epsilon_0} \cdot \frac{Q}{R} \]

where \( Q \) is the total charge on the shell and \( R \) is the radius of the shell.

6. **Conclusion**: Since the electric field inside the shell is zero, the potential inside the shell is constant and equal to the potential at the surface. However, the potential difference between any point inside the shell and the surface is zero, leading us to conclude that the potential inside the shell is effectively zero when considering the reference point at infinity.

### Final Answer:
The electric potential inside a spherical shell is zero.

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