A : The poynting vector given as `bar(S) = (bar(E ) xx bar( B))/(mu_0)` represents the instantaneous intensity at a point.
R : The velocity of an electromagnetic wave is in the direction of the vector `bar( E) xx bar (B)`.

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 the 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 solve the problem, we need to analyze the assertion and reason provided in the question.

### Step-by-Step Solution:

1. **Understanding the Poynting Vector**:
The Poynting vector \( \bar{S} \) is defined as:
\[ \bar{S} = \frac{\bar{E} \times \bar{B}}{\mu_0} \]
where \( \bar{E} \) is the electric field vector, \( \bar{B} \) is the magnetic field vector, and \( \mu_0 \) is the permeability of free space. This vector represents the instantaneous intensity of the electromagnetic wave at a point in space.

2. **Analyzing the Assertion**:
The assertion states that the Poynting vector represents the instantaneous intensity at a point. This is indeed true because the Poynting vector quantifies the power per unit area carried by the electromagnetic wave. Therefore, the assertion is correct.

3. **Understanding the Direction of Wave Propagation**:
The reason states that the velocity of an electromagnetic wave is in the direction of the vector \( \bar{E} \times \bar{B} \). According to the right-hand rule, if you point your fingers in the direction of \( \bar{E} \) and curl them towards \( \bar{B} \), your thumb will point in the direction of the wave's propagation (the velocity vector).

4. **Analyzing the Reason**:
The reason is also true because the direction of wave propagation is indeed given by the cross product \( \bar{E} \times \bar{B} \). However, while both statements are true, they do not explain each other. The assertion describes what the Poynting vector represents, while the reason describes the direction of wave propagation.

5. **Conclusion**:
Since both the assertion and reason are true but the reason does not explain the assertion, the correct answer is:
- Both assertion and reason are true, but the reason is not the correct explanation of the assertion.

### Final Answer:
The correct option is: Both assertion and reason are true, but reason is not the correct explanation of assertion.

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