Question

The pointing vector $\vec{P} = \vec{E} \times \vec{H}$ represents:

• A. Stored energy density in the electric field
• B. Stored energy density in the magnetic field
• C. The directional power flux density (power per unit area) of an electromagnetic wave
• D. The curl of the electric field

Hint:

$\vec{E} \times \vec{H}$ always represents energy flow in electromagnetic waves.

Answer 1

The Correct Option is C

Concept: The Poynting vector is a key concept in electromagnetism and is defined as: \[ \vec{P} = \vec{E} \times \vec{H} \] where:
• $\vec{E}$ = Electric field intensity
• $\vec{H}$ = Magnetic field intensity It represents the rate of energy transfer per unit area, i.e., power flow density.

Step 1: Physical Meaning The magnitude of the Poynting vector gives: \[ |\vec{P}| = \text{Power per unit area} \quad (W/m^2) \] The direction of $\vec{P}$ indicates the direction of propagation of the electromagnetic wave.

Step 2: Analyze Options
• Stored energy density (electric field): This is given by $\frac{1}{2}\epsilon E^2$, not by Poynting vector.
• Stored energy density (magnetic field): This is given by $\frac{1}{2}\mu H^2$.
• Directional power flux density: This matches exactly with the definition of the Poynting vector.
• Curl of electric field: This is related to Maxwell’s equations, not Poynting vector.

Step 3: Conclusion \[ \therefore \text{Correct answer is (C)} \]