A point charge `Q` is placed outside a hollow spherical conductor of radius `R` , at a distance `r (r gt R)` from its centre `C` . The field at `C` due to the induced charges on the conductor is

Options

A. Zero
B. `k (q)/((r - R)^(2))`
C. `k(Q)/(r^(2))`directed towards Q
D. `k(Q)/(r^(2))`, directed away form Q

Explanation

To solve the problem, we need to analyze the situation involving a point charge \( Q \) placed outside a hollow spherical conductor of radius \( R \). The distance from the center \( C \) of the sphere to the point charge \( Q \) is \( r \), where \( r > R \).

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a hollow spherical conductor with radius \( R \).
- A point charge \( Q \) is located outside this conductor at a distance \( r \) from the center \( C \) of the sphere, where \( r > R \).

2. **Electric Field Due to the Point Charge**:
- The point charge \( Q \) creates an electric field in the surrounding space. The electric field \( E \) at any point outside the sphere due to the charge \( Q \) is given by:
\[ E = \frac{kQ}{r^2} \]
- Here, \( k \) is Coulomb's constant.

3. **Induced Charges on the Conductor**:
- The presence of the external charge \( Q \) induces charges on the surface of the hollow conductor. The inner surface of the conductor will have an induced charge that creates an electric field that cancels the field due to \( Q \) within the conductor.

4. **Electric Field Inside the Conductor**:
- According to electrostatic shielding, the electric field inside a hollow conductor is zero when it is in electrostatic equilibrium. Therefore, the electric field at the center \( C \) of the sphere due to the induced charges must exactly cancel the electric field due to the external charge \( Q \).

5. **Field at Point C Due to Induced Charges**:
- Since the electric field inside the conductor is zero, the electric field at point \( C \) due to the induced charges must be equal in magnitude and opposite in direction to the electric field produced by the charge \( Q \) at that point. Thus, the electric field at \( C \) due to the induced charges is:
\[ E_{\text{induced}} = -\frac{kQ}{r^2} \]
- This field is directed towards the charge \( Q \).

6. **Conclusion**:
- The electric field at the center \( C \) due to the induced charges on the conductor is directed towards the charge \( Q \) and has a magnitude of:
\[ E_{\text{induced}} = \frac{kQ}{r^2} \]
- Therefore, the answer is that the field at \( C \) due to the induced charges on the conductor is directed towards \( Q \).

### Final Answer:
The field at \( C \) due to the induced charges on the conductor is directed towards the charge \( Q \).