If a solid and a hollow conducting sphere have same radius then

Options

A. Hollow sphere will hold more maximum charge
B. Solid sphere will hold more maximum charge
C. Both the spheres will hold same maximum charge
D. Both the sphere can't hold charge

Answer

To solve the problem regarding the solid and hollow conducting spheres with the same radius, we will analyze the distribution of electric charge on both spheres based on the principles of electrostatics.

### Step-by-Step Solution:

1. **Understanding Conductors**:
- In electrostatics, charges reside on the surface of conductors. This is because the electric field inside a conductor in electrostatic equilibrium is zero.

**Hint**: Remember that the electric field inside a conductor is always zero when it is in electrostatic equilibrium.

2. **Charge Distribution**:
- For both the solid and hollow conducting spheres, any charge \( Q \) placed on them will distribute itself uniformly over the surface. This is true for both types of conductors.

**Hint**: Consider how charges behave in a conductor and why they move to the surface.

3. **Electric Field Inside the Spheres**:
- According to Gauss's law, the electric field inside both the solid and hollow conducting spheres must be zero. Therefore, there is no charge enclosed within the Gaussian surface inside either sphere.

**Hint**: Use Gauss's law to understand the relationship between charge and electric field.

4. **Surface Charge Density**:
- Since both spheres have the same radius and are conducting, the surface charge density \( \sigma \) (charge per unit area) on both spheres will be the same if they carry the same total charge \( Q \).

**Hint**: Recall the formula for surface charge density: \( \sigma = \frac{Q}{A} \), where \( A \) is the surface area.

5. **Comparison of Charges**:
- Given that both spheres are identical in size and conducting, they can hold the same amount of charge. Therefore, if one sphere has a charge \( Q_1 \), the other must also have a charge \( Q_1 \).

**Hint**: Think about the implications of identical geometries and conducting properties on charge capacity.

6. **Conclusion**:
- The maximum charge that can be held by the solid sphere is equal to the maximum charge that can be held by the hollow sphere since they are both conducting and have the same radius.

**Hint**: Summarize your findings by stating that both spheres can hold the same maximum charge due to their identical nature.

### Final Answer:
Both the solid and hollow conducting spheres will hold the same maximum charge when they have the same radius.