A hollow sphere has charge density `.sigma.Cm^(-2)`. Identify incorrect statement

Options

A. Electric field inside sphere is zero
B. Electric field outside sphere is inversaly
C. Electric field on its surface is `(sigma)/(epsilon_(0))`
D. Electric feld sphere is inversly proportional to square of distance of that point from its centre.

Answer

To solve the question regarding the hollow sphere with charge density \(\sigma \, \text{C/m}^2\) and identify the incorrect statement, we will analyze the properties of electric fields related to hollow charged spheres.

### Step-by-Step Solution:

1. **Understanding the Hollow Sphere**:
A hollow sphere with a uniform surface charge density \(\sigma\) behaves according to the principles of electrostatics. The charge resides on the surface of the sphere.

**Hint**: Recall that for a hollow conductor, charges reside on the outer surface.

2. **Electric Field Inside the Sphere**:
Inside a hollow charged conductor, the electric field is zero. This is due to the symmetry of the charge distribution, which cancels out any electric field within the hollow region.

**Hint**: Remember Gauss's law and its implications for conductors.

3. **Electric Field Outside the Sphere**:
The electric field outside a uniformly charged hollow sphere behaves as if all the charge were concentrated at the center of the sphere. The electric field \(E\) at a distance \(r\) from the center (where \(r\) is greater than the radius \(R\) of the sphere) is given by:
\[ E = \frac{1}{4\pi \epsilon_0} \cdot \frac{Q}{r^2} \]
where \(Q\) is the total charge on the sphere.

**Hint**: Use the formula for the electric field due to a point charge and consider that the sphere acts like a point charge from outside.

4. **Electric Field on the Surface of the Sphere**:
The electric field just outside the surface of the sphere is given by:
\[ E = \frac{\sigma}{\epsilon_0} \]
This is derived from the surface charge density \(\sigma\).

**Hint**: Relate surface charge density to the electric field using Gauss's law.

5. **Analyzing Statements**:
Now, we need to evaluate the statements provided in the question:
- **Statement 1**: The electric field inside the conductor is zero. (True)
- **Statement 2**: The electric field outside the sphere is inversely proportional to the square of the distance from the center. (True)
- **Statement 3**: The electric field on the surface is \(\frac{\sigma}{\epsilon_0}\). (True)
- **Statement 4**: The electric field of the sphere is inversely proportional to the square of the distance from the center. (True)

Since all statements appear to be true, we need to identify if any statement is incorrectly phrased or misleading.

6. **Conclusion**:
If all statements are indeed true, then the question may be incorrectly framed or there might be a misunderstanding in the interpretation of the statements. However, based on the analysis, if any statement were to be considered incorrect, it would be one that misrepresents the properties of the electric field in relation to the hollow sphere.

### Final Answer:
All statements provided in the question regarding the hollow sphere are correct based on the principles of electrostatics.