The poynting vector in vaccum is represented by (where symbols have their usual meanings)

Options

A. `(vec B × vec E)/(mu_0)`
B. `(vec E × vec B)/(mu_0)`
C. `(vec E × vec B) /(mu_0 × epsilon_0)`
D. `(vec B × vec E)/(mu_0 × epsilon_0)`

Answer

To solve the question regarding the Poynting vector in vacuum, we will follow these steps:

### Step 1: Understand the Poynting Vector
The Poynting vector (S) is a vector that represents the directional energy flux (the rate of energy transfer per unit area) of an electromagnetic field. It is defined as the cross product of the electric field vector (E) and the magnetic field vector (B), scaled by the permeability of free space (μ₀).

### Step 2: Write the Formula
The formula for the Poynting vector in vacuum is given by:

\[ \mathbf{S} = \frac{1}{\mu_0} \mathbf{E} \times \mathbf{B} \]

Where:
- \( \mathbf{S} \) is the Poynting vector,
- \( \mathbf{E} \) is the electric field vector,
- \( \mathbf{B} \) is the magnetic field vector,
- \( \mu_0 \) is the permeability of free space.

### Step 3: Analyze the Components
- The cross product \( \mathbf{E} \times \mathbf{B} \) gives a vector that is perpendicular to both the electric and magnetic fields, indicating the direction of energy flow.
- The factor \( \frac{1}{\mu_0} \) ensures that the units of the Poynting vector are in watts per square meter (W/m²), which is the SI unit for power per unit area.

### Step 4: Conclusion
Thus, the Poynting vector in vacuum can be succinctly represented as:

\[ \mathbf{S} = \frac{1}{\mu_0} \mathbf{E} \times \mathbf{B} \]