a) The (covariant) Lagrangian of a particle interacting with an electromagnetic field is given byL (x, u) == -mc\/ubuzUse the Lagrange equationsd dLƏLdт дияto derive the equation of motionduamdtHere we have used the tensor Faß = JªA³ – ƏB Aª.b) The Lagrangian (density) of the electromagnetic field is given by1L (ª A® , A® , x)-Faß Faß16тAª ja-Use the Lagrange equationsƏLƏLdxa d(dª A®)to derive the inhomogeneous Maxwell equationsJ Faß

We need to show that-(a) Derive equation of motion,mduαdτ=qcFαβuβ(b) Deive inhomogeneous maxwell…

a) The (covariant) Lagrangian of a particle interacting with an electromagnetic field is given by L (x, u) = -mc₁√√/u³ uz Use the Lagrange equations to derive the equation of motion d ƏL dr Jua dua dT с Here we have used the tensor Faß = Jª A³ - ³ Aª. m Use the Lagrange equations L (№ª A³, A³, x) = == b) The Lagrangian (density) of the electromagnetic field is given by 1 ƏL əxa to derive the inhomogeneous Maxwell equations Ja Faß 1 16п Faß up. = ә ƏL ƏL дха д(дº AB) AB с -Faß Fa = 4π js. Aªua. Faß Aa aja.

a) The (covariant) Lagrangian of a particle interacting with an electromagnetic field is given by L (x, u) = -mc₁√√/u³ uz Use the Lagrange equations to derive the equation of motion d ƏL dr Jua dua dT с Here we have used the tensor Faß = Jª A³ - ³ Aª. m Use the Lagrange equations L (№ª A³, A³, x) = == b) The Lagrangian (density) of the electromagnetic field is given by 1 ƏL əxa to derive the inhomogeneous Maxwell equations Ja Faß 1 16п Faß up. = ә ƏL ƏL дха д(дº AB) AB с -Faß Fa = 4π js. Aªua. Faß Aa aja.