Define the Poynting vector and interpret its physical meaning.

Define the Poynting vector and interpret its physical meaning.

• A. S = E × H; energy flow per unit area; power crossing a surface per unit time
• B. S = E × B; energy density
• C. S = E · H; energy transport speed
• D. S = H × D; energy flux

Answer: (A)

The Poynting vector represents how electromagnetic energy flows through space and per unit area. It is defined as the cross product of the electric field and the magnetic field intensity: S = E × H. This vector points in the direction in which the energy is traveling, and its magnitude tells you how much energy crosses a given area per unit time. In SI units, S has units of watts per square meter, so the total power crossing a surface is found by integrating S over that surface, P = ∬ S · dA. For a plane wave in vacuum, E, H, and the direction of propagation are all perpendicular, so S points along the propagation direction and its magnitude is the energy-flux density. Why this definition fits: the energy in the electromagnetic field is stored in both the electric and magnetic fields, but the rate at which that energy moves through space is captured by the cross product E × H, which naturally encodes both the field strengths and their perpendicular orientations. The other expressions listed don’t describe a vector energy flux with the correct physical meaning: E × B would be related to the flux but involves B instead of H (and the units don’t match without extra factors), E · H is a scalar, and H × D isn’t the standard energy flow quantity.

The Poynting vector represents how electromagnetic energy flows through space and per unit area. It is defined as the cross product of the electric field and the magnetic field intensity: S = E × H. This vector points in the direction in which the energy is traveling, and its magnitude tells you how much energy crosses a given area per unit time.

In SI units, S has units of watts per square meter, so the total power crossing a surface is found by integrating S over that surface, P = ∬ S · dA. For a plane wave in vacuum, E, H, and the direction of propagation are all perpendicular, so S points along the propagation direction and its magnitude is the energy-flux density.

Why this definition fits: the energy in the electromagnetic field is stored in both the electric and magnetic fields, but the rate at which that energy moves through space is captured by the cross product E × H, which naturally encodes both the field strengths and their perpendicular orientations. The other expressions listed don’t describe a vector energy flux with the correct physical meaning: E × B would be related to the flux but involves B instead of H (and the units don’t match without extra factors), E · H is a scalar, and H × D isn’t the standard energy flow quantity.