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 assertion-reason question, we will analyze both the assertion (A) and the reason (R) step by step.

### Step 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. The Poynting vector represents the directional energy flux, or the energy per unit area per unit time, of an electromagnetic wave.

### Step 2: Direction of the Poynting Vector
The direction of the Poynting vector \( \bar{S} \) is given by the cross product \( \bar{E} \times \bar{B} \). The direction of this vector indicates the direction in which energy is flowing.

### Step 3: Relationship Between \( \bar{E} \), \( \bar{B} \), and Wave Propagation
For electromagnetic waves, the direction of propagation is given by the vector \( \bar{E} \times \bar{B} \). This means that the wave travels in the direction of the Poynting vector, which is also the direction of the cross product \( \bar{E} \times \bar{B} \).

### Step 4: Analyzing the Assertion (A)
The assertion states that the Poynting vector represents the instantaneous intensity at a point. This is correct because the Poynting vector indeed quantifies the energy flow per unit area, which can be interpreted as intensity.

### Step 5: Analyzing the Reason (R)
The reason states that the velocity of an electromagnetic wave is in the direction of the vector \( \bar{E} \times \bar{B} \). This is also correct, as the direction of wave propagation is aligned with the direction of the Poynting vector, which is given by the cross product of the electric and magnetic fields.

### Step 6: Conclusion
Both the assertion and the reason are correct. However, the reason does not serve as a direct explanation for the assertion since the assertion is based on the definition of the Poynting vector, while the reason describes the direction of wave propagation.

### Final Answer
- Assertion (A) is correct.
- Reason (R) is correct.
- However, (R) is not the correct explanation for (A).