Assertion : Two concentric spherical shells A and B are charged by charges `q_(A)` and `q_(B)`. If `q_(A)` is negative, then `V_(A)-V_(B)` is also negative.
Reason : `V_(A)-V_(B) =(q_(A)/(4pi epsi_(0)))(1/R_(A)-1/r_(B))`
therefore, if `q_(A)` is negative, then `V_(A)-V_(B)` is also negative.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the problem, we need to analyze both the assertion and the reason given in the question.

### Step 1: Understanding the Assertion
The assertion states that if two concentric spherical shells A and B are charged with charges \( q_A \) and \( q_B \), and if \( q_A \) is negative, then \( V_A - V_B \) is also negative.

### Step 2: Understanding the Reason
The reason provided is the formula for the potential difference between the two shells:
\[ V_A - V_B = \left( \frac{q_A}{4 \pi \epsilon_0} \right) \left( \frac{1}{R_A} - \frac{1}{R_B} \right) \]
This equation shows how the potential difference depends on the charges and the radii of the shells.

### Step 3: Analyzing the Formula
1. **Identify the terms**:
- \( q_A \) is the charge on shell A, which is given to be negative.
- \( R_A \) and \( R_B \) are the radii of shells A and B, respectively.

2. **Substituting the charge**:
Since \( q_A \) is negative, the term \( \frac{q_A}{4 \pi \epsilon_0} \) will also be negative.

3. **Analyzing the expression**:
- The term \( \left( \frac{1}{R_A} - \frac{1}{R_B} \right) \) will depend on the radii of the shells.
- If \( R_A < R_B \), then \( \frac{1}{R_A} > \frac{1}{R_B} \), making the term positive.
- If \( R_A > R_B \), then \( \frac{1}{R_A} < \frac{1}{R_B} \), making the term negative.

### Step 4: Conclusion on \( V_A - V_B \)
- If \( R_A < R_B \), \( V_A - V_B \) will be negative because a negative \( q_A \) multiplied by a positive term results in a negative value.
- If \( R_A > R_B \), \( V_A - V_B \) could be positive or negative depending on the magnitude of the terms.

### Step 5: Final Evaluation
Since the assertion states that \( V_A - V_B \) is negative when \( q_A \) is negative, and the reason correctly explains the relationship between the charges and the potential difference, we conclude that both the assertion and the reason are correct.

### Final Answer
Both the assertion and the reason are correct.

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