A static charge distribution (r) generates an electric field E(r) in the frame K ' Set the distribution into motion with velocity v x as viewed from the laboratory frame K (a) Let u EM be the electromagnetic energy density Show that u EM t ' 0 Use this fact to show that S 0 u EM t 0 in K where S 0 ...

To solve this problem we need to use the equations of electromagnetism in both frames K and K and apply Lorentz transformations Lets go step by step a First lets express the electromagnetic energy den ...

A static charge distribution (r) generates an electric field E(r) in the frame K'. Set the distribution

Question:

A static charge distribution ρ(r) generates an electric field E(r) in the frame K'. Set the distribution into motion with velocity v = νx̂ as viewed from the laboratory frame K.

(a) Let u_EMbe the electromagnetic energy density. Show that ∂u_EM/∂t' = 0. Use this fact to show that ∇ · S₀+ ∂u_EM/∂t = 0 in K where S₀ = u_EMv.
(b) Show that the Poynting vector, S = E × B/μ₀, is not equal to S0, but that ∇ · S = ∇ · S₀.