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 step by step, we need to analyze the situation of a conducting sphere with a spherical cavity and a point charge placed within that cavity. The charge is then shifted to the center of the cavity. Let's break down the solution:

### Step 1: Understand the System
We have a conducting sphere of radius \( R_2 \) with a spherical cavity of radius \( R_1 \) that is non-concentric with the sphere. A point charge \( q_1 \) is initially placed at a distance \( r \) from the center of the cavity.

**Hint:** Visualize the arrangement of the conducting sphere and the cavity to understand how the charge affects the electric field and potential.

### Step 2: Initial Conditions
When the charge \( q_1 \) is placed at a distance \( r \) from the center of the cavity, it induces a charge on the inner surface of the cavity. The conducting material will redistribute its free charges to maintain electrostatic equilibrium.

**Hint:** Remember that the electric field inside a conductor in electrostatic equilibrium is zero, and the induced charge on the cavity surface will depend on the position of \( q_1 \).

### Step 3: Shift the Charge to the Center
Now, we shift the charge \( q_1 \) to the center of the cavity. This change will affect the distribution of the induced charge on the inner surface of the cavity.

**Hint:** Consider how the symmetry of the charge distribution changes when \( q_1 \) is moved to the center.

### Step 4: Analyze the Electric Field Outside the Sphere
According to Gauss's law, the electric field outside the conducting sphere depends only on the total charge enclosed within the Gaussian surface. Since the total charge on the conducting sphere remains constant, the electric field outside the sphere does not change when \( q_1 \) is moved.

**Hint:** Use Gauss's law to conclude that the electric field outside the conducting sphere remains unchanged.

### Step 5: Analyze the Electric Potential Outside the Sphere
Since the electric field outside the sphere does not change, the electric potential outside the sphere also remains constant.

**Hint:** Recall that electric potential is related to electric field through the relationship \( E = -\frac{dV}{dr} \).

### Step 6: Electrostatic Energy in the System
The electrostatic energy stored in the system is related to the configuration of the charges. When \( q_1 \) is moved to the center, the potential energy associated with the charge configuration may change due to the change in the potential at the location of the charge.

**Hint:** Consider how the potential energy depends on the position of the charge within the cavity.

### Step 7: Electric Potential of the Sphere
The conducting sphere maintains an equipotential surface. The potential of the sphere does not change because the charge distribution on the surface remains uniform regardless of the position of \( q_1 \).

**Hint:** Remember that the potential on the surface of a conductor in electrostatic equilibrium is constant.

### Conclusion
Based on the analysis:
- The electric field outside the sphere does not change.
- The electric potential outside the sphere does not change.
- The electrostatic energy in the system may change when \( q_1 \) is moved to the center.
- The electric potential of the sphere remains constant.

Thus, the correct alternative is that the electrostatic energy stored in the system may change.

### Final Answer
The correct alternative is: **Electrostatic energy stored in the system may change.**