In the above question, if Q' is removed then which option is correct :

Options

A.
B.
C.
D.

Answer

To solve the problem, we need to analyze the situation when the external charge \( Q' \) is removed from the system. Let's break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- We have a charge \( q \) placed at the center of a conducting spherical shell with radius \( R \).
- The shell itself has a charge \( q \).
- There is an external charge \( Q' \) located at a distance \( r' \) from the charge \( q \).

2. **Effect of the Conducting Shell**:
- The conducting shell will redistribute its charge in response to the charge \( q \) at its center.
- The inner surface of the shell will acquire a charge of \(-q\) to neutralize the electric field inside the conductor.
- The outer surface of the shell will then have a charge of \( q + q \) (the charge on the shell plus the induced charge), resulting in a total charge of \( 2q \).

3. **Electric Field Inside the Shell**:
- Inside the conducting shell (at a distance \( r < R \)), the electric field is zero due to electrostatic shielding.
- This means that any point inside the shell does not experience any electric field from the external charge \( Q' \) or the shell itself.

4. **Removing the External Charge \( Q' \)**:
- When the external charge \( Q' \) is removed, the situation inside the shell remains unchanged.
- The charge \( q \) at the center still induces a charge of \(-q\) on the inner surface of the shell, and the outer surface still has a charge of \( 2q \).

5. **Resultant Electric Field at Distance \( r < R \)**:
- Since the electric field inside the conductor remains zero regardless of the presence of the external charge \( Q' \), removing \( Q' \) does not affect the electric field at a distance \( r < R \).
- Therefore, the electric field at any point inside the shell (for \( r < R \)) remains zero.

### Conclusion:
Thus, the correct option when \( Q' \) is removed is that the electric field inside the conducting shell (at a distance \( r < R \)) remains zero.