A conducting sphere of radius `R_(2)` has a spherical cavity of radius `R_(1)` which is non concentric with the sphere. A point charge `q_(1)` is placed at a distance r from the centre of the cavity. For this arrangement, answer the following questions.
If `q_(1)` is shifted to the centre of the cavity, then: (choose the correct alternative)

Options

A. electric field in the region outside sphere may change
B. electric potential in the region outside sphere may change
C. electrostatic energy stored in the system may change
D. electric potential of sphere may change

Explanation

To solve the problem, we need to analyze the situation step by step, focusing on the effects of moving the point charge \( q_1 \) to the center of the cavity within a conducting sphere.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a conducting sphere of radius \( R_2 \) with a spherical cavity of radius \( R_1 \).
- A point charge \( q_1 \) is initially placed at a distance \( r \) from the center of the cavity.

2. **Initial Charge Distribution**:
- When the charge \( q_1 \) is placed at distance \( r \) from the center of the cavity, it induces a charge on the inner surface of the cavity. The induced charge will be negative and equal to \( -q_1 \).
- Consequently, a positive charge \( +q_1 \) will appear on the outer surface of the conducting sphere to maintain overall neutrality.

3. **Moving \( q_1 \) to the Center**:
- When \( q_1 \) is moved to the center of the cavity, the charge distribution on the inner surface of the cavity will still be \( -q_1 \) because the charge \( q_1 \) remains the same.
- The outer surface will still have a charge of \( +q_1 \).

4. **Electric Field Inside the Cavity**:
- The electric field inside a conductor is zero. Therefore, the electric field in the conducting material remains zero.
- The electric field inside the cavity (where \( q_1 \) is now at the center) can be calculated using Gauss's law. The electric field will be uniform and directed outward from the charge \( q_1 \).

5. **Electric Field Outside the Sphere**:
- The electric field outside the conducting sphere is determined only by the total charge on the outer surface, which remains \( +q_1 \).
- Therefore, the electric field in the region outside the sphere does not change when \( q_1 \) is moved to the center.

6. **Electric Potential**:
- The electric potential inside the cavity will change because the distance from the point charge \( q_1 \) to any point in the cavity changes.
- The potential at any point in the cavity when \( q_1 \) is at the center will be different from when it was at distance \( r \).

7. **Electrostatic Energy**:
- The electrostatic energy stored in the system may change due to the change in potential distribution when \( q_1 \) is moved to the center.

### Conclusion:
Based on the analysis, the correct alternatives regarding the effects of moving \( q_1 \) to the center of the cavity are:
- The electric field in the region outside the sphere does not change.
- The electric potential in the cavity changes.
- The electrostatic energy stored in the system may change.