Relativistic electrodynamics (10 Points) Working in natural units, recall that the electric and magnetic fields are related to the vector and scalar potentials by E = -V6-0, A B = VAA We have defined the 4- potential A = (0, A) and the 4-divergence 0 = (0,7), also the 4-current J = (p.3) Hint: Repeated induces are summed over and u,v.. € 0,1,2,3 1. Charge conservation implies the continuity equation Op+7= 0, show that it could be written in the Lorentz index notation ₁J"=0 2. Show that the Faraday tensor defined as F = OA-OA,, takes the matrix form 0 E₁ E₂ E3 -E₁ 0 -B3 B₂ -E₂ B3 0 -B₁ -E3-B₂ B₁ 0 F Hint: Observe that the vector product in index notation can be expressed as (a^b) = €₁jka¹b² = (a, b, -a; b)kijk € 1,2,3