(a) Calculate F = A A from the Lienard-Wiechert...

(a) Calculate F_μν = ∂_μA_ν − ∂_νA_μ from the Li´enard-Wiechert potential Aμ. Express the result in terms of Rμ, the four-velocity U_μ, and the four-acceleration ∂U_μ/∂τ . It will be useful to evaluate ∂_μ(R_σR_σ) in order to show that ∂_μτ = R_μ/(R_σU_σ).
(b) Show that the splitting of F_μν into a velocity part and an acceleration part is relativistically invariant.
(c) Find E and B when v = 0 (but v̇ ≠ 0) by evaluating appropriate components of F_μν in the rest frame of the charge.