(A) : Electromagnetic waves are tranverse in nature. (R) : The Poynting,s vector which gives the power density is given by `vecP=vecExxvecB`

Options

A. Both 'A' and 'R' are true and 'R' is the correct explanation of 'A'.
B. Both 'A' and ’R' are true and 'R' is not the correct explanation of 'A
C. A' is true and 'R' is false
D. 'A' is false and R' is true

Answer

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that "Electromagnetic waves are transverse in nature."

**Explanation:**
- Electromagnetic waves consist of oscillating electric (E) and magnetic (B) fields that are perpendicular to each other and to the direction of wave propagation.
- This characteristic of oscillation perpendicular to the direction of travel is what defines them as transverse waves.

### Step 2: Analyze the Reason
The reason states that "The Poynting vector, which gives the power density, is given by \(\vec{P} = \vec{E} \times \vec{B}\)."

**Explanation:**
- The Poynting vector \(\vec{P}\) represents the directional energy flux (the rate of energy transfer per unit area) of an electromagnetic field.
- The correct expression for the Poynting vector is \(\vec{P} = \frac{1}{\mu_0} \vec{E} \times \vec{B}\), where \(\mu_0\) is the permeability of free space.
- The reason provided in the question is incomplete and does not accurately describe the Poynting vector.

### Step 3: Conclusion
Based on the analysis:
- The assertion is **true** because electromagnetic waves are indeed transverse in nature.
- The reason is **false** because it does not correctly express the Poynting vector.

Thus, the correct answer is that the assertion is true and the reason is false.

### Final Answer:
Assertion (A) is true, and Reason (R) is false.

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