Question

2 Coulomb Gauge Besides the Lorenz gauge, another typical gauge choice is the Coulomb gauge, defined by a) 2 Points] Is this gauge choice Lorentz invariant, i.e. is it the same for all reference frames? Justify your answer. Hint: It sufices to find a good reasoning here, so you don't necessarily need to compute anything but feel free to do so if you want). b) /2 Points/ Find a condition for x(2) in the Coulomb gauge, such that leaves the Lagrangian density invariant A0(z) and the vector c) /3 Points/ Find the equations of motion for the scalar potential φ(z) potential A(z) Ξ {A' (2), 1-1 ,2,3} in the Coulomb gauge d) 3 Points/ Show that is a valid gauge choice in the Coulomb gauge for a uniform and constant (i.e. B(t, const) magnetic field Hint: You have to check both, that this choice fulfils the Coulomb gauge condition and that the resulting electric and magnetic fields obey the Marwell equations

Answer 1

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