In the following question a statement of assertion (A) is followed by a statement of reason (R )
A: the potential difference between two concentric spherical shells depends only on the charge of inner shell
R : the electric field in the region in between two shells depedns on the charge of inner shell and electric field is the negative of potential gradient.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark (1).
B. If both Assertion & Reason are true but the reason is not correct explanation of the assertion then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements , then mark (4).

Answer

To analyze the given assertion (A) and reason (R), let's break down the concepts involved step by step.

### Step 1: Understanding the Assertion (A)
The assertion states that "the potential difference between two concentric spherical shells depends only on the charge of the inner shell."

**Explanation:**
- For concentric spherical shells, the electric field in the region between the shells is generated by the charge on the inner shell.
- The potential difference (V) between the two shells can be calculated using the formula:
\[ V = -\int E \cdot dr \]
- In the case of spherical shells, the electric field (E) between the shells is given by:
\[ E = \frac{1}{4\pi \epsilon_0} \frac{Q}{r^2} \]
where \( Q \) is the charge on the inner shell and \( r \) is the distance from the center.

### Step 2: Understanding the Reason (R)
The reason states that "the electric field in the region in between two shells depends on the charge of the inner shell and the electric field is the negative of the potential gradient."

**Explanation:**
- The electric field (E) indeed depends on the charge of the inner shell, as shown in the formula above.
- The relationship between electric field and potential gradient is given by:
\[ E = -\frac{dV}{dr} \]
This means that the electric field is related to how the electric potential (V) changes with respect to distance (r).

### Step 3: Conclusion
Now, let's evaluate the truth of both statements:
- The assertion (A) is **true** because the potential difference between the shells is determined by the charge on the inner shell.
- The reason (R) is also **true** as the electric field indeed depends on the charge of the inner shell and is related to the potential gradient.

### Final Evaluation
Since both the assertion and the reason are true, and the reason correctly explains the assertion, we conclude that the statement is valid.

### Summary
- **Assertion (A)**: True
- **Reason (R)**: True
- **Conclusion**: R explains A, hence the assertion is correct.

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