Question

The Poynting vector in electromagnetic theory represents,

• A. The electric field strength at a point
• B. The rate at which energy is transported by the electromagnetic wave
• C. The potential energy in the electric field
• D. The time-averaged power dissipated in a resistor

Hint:

The direction of the Poynting vector $\mathbf{S} = \mathbf{E} \times \mathbf{H}$ points exactly along the line of wave propagation. It tells you two critical parameters at once: where the wave energy is headed, and how concentrated that power is per square meter.

Answer 1

The Correct Option is B

Concept: The Poynting vector, conventionally denoted as $\mathbf{S}$, represents the directional power flux density of an electromagnetic wave. It is defined mathematically as the cross-product of the Electric Field vector ($\mathbf{E}$) and the Magnetic Field intensity vector ($\mathbf{H}$): $$\mathbf{S} = \mathbf{E} \times \mathbf{H}$$ Step-by-step Dimensional Analysis and Physical Interpretation:
• Let us evaluate the dimensional units of the vectors involved: E & arrow Volts per meter (\frac{V}{m})
H & arrow Amperes per meter (\frac{A}{m})
• Performing the cross-product operation combines these units together: $$\text{Units of } \mathbf{S} = \left(\frac{\text{V}}{\text{m}}\right) \times \left(\frac{\text{A}}{\text{m}}\right) = \frac{\text{V} \cdot \text{A}}{\text{m}^2}$$
• Since Power (in Watts) equals Voltage ($\text{V}$) multiplied by Current ($\text{A}$): $$\text{Units of } \mathbf{S} = \frac{\text{Watts}}{\text{meter}^2} \quad \left(\frac{\text{W}}{\text{m}^2}\right)$$
• A unit of $\frac{\text{Watts}}{\text{m}^2}$ signifies the rate of energy transfer passing through a unit cross-sectional surface area perpendicular to the direction of wave propagation.