Comparing the Classical and Geometric Algebra representations of electromagnetic energy flow.
The Poynting vector (S) is calculated from the cross product of the E and B fields. It represents the linear flow of energy.
In the complex formalism, the Poynting vector has both real and imaginary parts. The imaginary component, related to reactive energy, is typically discarded as it has no direct physical analog for energy flow in free space.
The yellow square represents the Poynting Bivector (E ∧ B), the fundamental object of energy flow in Geometric Algebra.
S = E × B. Energy flows as a simple vector.
E = E₀ eiωt