A charge Q is kept at the centre of a conducting sphere of inner radius `R_(1)` and outer radius `R_(2)`. A point charge q is kept at a distance `r(gt R_(2))` from the centre. If q experiences an electrostatic force 10 N then assuming that no other charges are present, electrostatic force experienced by Q will be :

Options

A. `-10 N`
B. `0`
C. `20 N`
D. none of these

Answer

To solve the problem, we need to analyze the situation involving the charge \( Q \) at the center of a conducting sphere and the point charge \( q \) located outside the sphere.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a conducting sphere with an inner radius \( R_1 \) and an outer radius \( R_2 \).
- A charge \( Q \) is placed at the center of this conducting sphere.
- A point charge \( q \) is located at a distance \( r \) from the center, where \( r > R_2 \).

2. **Electrostatic Force on Charge \( q \)**:
- It is given that the charge \( q \) experiences an electrostatic force of \( 10 \, \text{N} \). This force is due to the electric field created by the charge \( Q \) and any induced charges on the conducting sphere.

3. **Properties of Conducting Spheres**:
- In a conductor, the electric field inside the conducting material is zero when in electrostatic equilibrium. Therefore, the electric field inside the conducting sphere (between \( R_1 \) and \( R_2 \)) is zero.
- The charge \( Q \) at the center will induce a charge on the inner surface of the sphere equal to \( +Q \) and an equal and opposite charge of \( -Q \) on the outer surface.

4. **Electric Field Outside the Sphere**:
- For points outside the conducting sphere (where \( r > R_2 \)), the conducting sphere behaves as if all the charge were concentrated at its center. Thus, the electric field \( E \) at a distance \( r \) from the center can be given by:
\[ E = \frac{kQ}{r^2} \]
- The force \( F \) on the charge \( q \) can be expressed as:
\[ F = qE = q \cdot \frac{kQ}{r^2} \]
- Given that \( F = 10 \, \text{N} \), we can use this information to understand the effect on \( Q \).

5. **Force on Charge \( Q \)**:
- Since the electric field inside the conductor is zero, the charge \( Q \) does not experience any electrostatic force due to the charge \( q \) located outside the conducting sphere.
- Therefore, the electrostatic force experienced by charge \( Q \) is:
\[ F_Q = 0 \, \text{N} \]

### Final Answer:
The electrostatic force experienced by charge \( Q \) will be \( 0 \, \text{N} \).

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