A solid conducting object with a non-uniform curvature is given a charge Q. Select the correct option.

Options

A. Charge will be uniformly distributed on its outer surface
B. Charge will be uniformly distributed over its volume
C. Charge will be non-uniformly distributed over its outer surface with more concentration of charge where the radius of curvature is small
D. Charge will be non-uniformly distributed over its outer surface with more concentration of charge where the radius of curvature is large

Answer

To solve the question regarding the charge distribution on a solid conducting object with non-uniform curvature, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Charge Distribution on Conductors**:
- In a conductor, electric charges are free to move. When a charge \( Q \) is given to a solid conducting object, the charges will redistribute themselves until electrostatic equilibrium is reached.

**Hint**: Remember that charges in a conductor move until they reach a state where the electric field inside the conductor is zero.

2. **Surface Charge Distribution**:
- The charges will reside on the surface of the conductor. This is because charges repel each other and will move as far apart as possible, which is on the surface.

**Hint**: Think about why charges prefer to be on the surface rather than inside the conductor.

3. **Non-Uniform Curvature**:
- Since the object has a non-uniform curvature, the radius of curvature (ROC) varies at different points on the surface. The surface charge density \( \sigma \) (charge per unit area) is related to the radius of curvature.

**Hint**: Recall that the surface charge density is influenced by the geometry of the conductor.

4. **Relationship Between Charge Density and Radius of Curvature**:
- The surface charge density \( \sigma \) is inversely proportional to the radius of curvature (ROC):
\[ \sigma \propto \frac{1}{\text{ROC}} \]
- This means that where the radius of curvature is small (sharp edges or points), the surface charge density will be high. Conversely, where the radius of curvature is large (flatter areas), the surface charge density will be low.

**Hint**: Consider how sharp edges can accumulate more charge compared to flatter surfaces.

5. **Conclusion on Charge Distribution**:
- Therefore, the charge distribution on the surface of the conductor will be non-uniform. There will be a higher concentration of charge where the radius of curvature is smaller, and a lower concentration where the radius of curvature is larger.

**Hint**: Visualize the conductor and imagine how charges would distribute themselves based on the shape.

### Final Answer:
The correct option is: **Charge will be non-uniformly distributed over its outer surface with more concentration of charges where the radius of curvature is small.**