Assertion:- Any arbitrary displacement of charges inside a shell does not introduce any change in the electrostatic field of the outer space.
Reason:- A closed conducting shell divides the entire space into the inner and outer parts which are completely independent of one another in respect of electric fields.

Options

A. If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.
B. If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.
C. If Assertion is True but the Reason is False.
D. If both Assertion `&` Reason are False.

Answer

**Solution:**

1. **Understanding the Assertion**: The assertion states that any arbitrary displacement of charges inside a conducting shell does not change the electrostatic field in the outer space. This is based on the principle of electrostatic shielding.

2. **Electrostatic Shielding**: When charges are placed inside a closed conducting shell, the shell redistributes its surface charges in response to the internal charges. This redistribution ensures that the electric field inside the conducting material of the shell is zero, and consequently, the electric field outside the shell remains unaffected by the internal charges.

3. **Gauss's Law Application**: According to Gauss's Law, the electric field outside a closed conductor depends only on the total charge enclosed within that conductor. If the charges inside the shell are displaced, the surface charges on the shell will rearrange themselves, but the total charge enclosed remains the same. Therefore, the electric field outside the shell remains unchanged.

4. **Understanding the Reason**: The reason states that a closed conducting shell divides the space into inner and outer parts that are independent of each other concerning electric fields. This is true because the electric field inside the conductor is zero, and any external electric field does not penetrate the conductor.

5. **Conclusion**: Both the assertion and the reason are true. The reason correctly explains the assertion, as the independence of the inner and outer electric fields is a direct consequence of electrostatic shielding.

**Final Answer**: Both the assertion and the reason are true, and the reason is the correct explanation for the assertion.

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