Given below are two statements :
Statement I : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.
Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius `r (lt R)` is zero but the electric flux passing through this closed spherical surface of radius r is not zero.
In the light of the above statements, choose the correct answer from the options given below :

Options

A. Both Statement I and Statement II are true
B. Statement I is true but Statement II is false
C. Both Statement I and Statement II are false
D. Statement I is false but Statement II is true.

Answer

To solve the problem, we need to analyze both statements and determine their validity based on the principles of electrostatics.

### Step-by-Step Solution:

**Step 1: Analyze Statement I**
- An electric dipole consists of two equal and opposite charges separated by a small distance.
- When an electric dipole is placed at the center of a hollow sphere, the electric field produced by the dipole at any point inside the sphere is not zero. The electric field lines will emanate from the positive charge and terminate at the negative charge.
- However, when calculating the electric flux through the surface of the sphere, we use Gauss's Law, which states that the electric flux (Φ) through a closed surface is proportional to the enclosed charge (Q_enc).
- Since the dipole has no net charge (the positive and negative charges cancel each other), the total enclosed charge is zero. Therefore, the electric flux through the hollow sphere is zero.

**Conclusion for Statement I**: True. The electric field is not zero inside the sphere, but the electric flux through the sphere is zero.

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**Step 2: Analyze Statement II**
- For a solid metallic sphere with total charge Q, the electric field inside the conductor (at any point where r < R) is zero due to electrostatic shielding. This means that if you are inside the metallic sphere, you will not experience any electric field.
- However, when considering a closed spherical surface of radius r (where r < R), we need to consider the charge on the sphere.
- The electric flux through this closed surface can be calculated using Gauss's Law. The total charge enclosed by this surface is zero because there is no charge inside the conductor (the charge resides on the surface).
- Therefore, the electric flux through this closed surface is also zero.

**Conclusion for Statement II**: False. The electric field inside the metallic sphere is zero, and the electric flux through the closed surface of radius r is also zero.

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### Final Answer:
- **Statement I**: True
- **Statement II**: False