Assertion (A) A charge q is placed on a height h/4 above the centre of a square of side b . The fluk associated with the square is independent of side length.
Reason (R ) Gauss 's law is independent of size of the Gaussian surface.

Options

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

Answer

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

### Step 1: Understanding the Assertion (A)
The assertion states that a charge \( q \) is placed at a height \( \frac{h}{4} \) above the center of a square of side \( b \). It claims that the electric flux associated with the square is independent of the side length \( b \).

### Step 2: Applying Gauss's Law
According to Gauss's Law, the electric flux \( \Phi \) through a closed surface is given by:
\[ \Phi = \frac{Q_{\text{enc}}}{\epsilon_0} \]
where \( Q_{\text{enc}} \) is the charge enclosed by the surface and \( \epsilon_0 \) is the permittivity of free space.

### Step 3: Analyzing the Charge Configuration
In this scenario, the square is not a closed surface, but we can consider the electric field due to the charge \( q \) at the height \( \frac{h}{4} \). The electric field produced by the charge \( q \) will be uniform over the square surface if the distance from the charge to the square is much larger than the dimensions of the square.

### Step 4: Independence of Side Length
The assertion claims that the flux through the square is independent of the side length \( b \). This is true because the electric flux depends only on the charge \( q \) and not on the area of the square. Thus, as long as the charge \( q \) remains constant, the flux through the square will also remain constant regardless of the size of the square.

### Step 5: Understanding the Reason (R)
The reason states that Gauss's Law is independent of the size of the Gaussian surface. This is also correct because Gauss's Law relates the electric flux through a closed surface to the charge enclosed within that surface, not to the dimensions of the surface itself.

### Conclusion
Both the assertion (A) and the reason (R) are correct. Furthermore, the assertion provides a correct explanation for the reason.

### Final Answer
Both the assertion and the reason are correct, and the assertion is the correct explanation of the reason.

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