Let = A + (1/c 2 )/t. Fermi showed that one can use a Lagrange parameter to impose the Lorenz gauge

Let Ω = ∇ · A + (1/c²)∂ϕ/∂t. Fermi showed that one can use a Lagrange parameter λ to impose the Lorenz gauge condition Ω = 0 using the Lagrangian density

(a) Show that the Lagrange equations for the potentials are modified inhomogeneous wave equations.

(b) Find the corresponding modified inhomogeneous Maxwell equations.

(c) Manipulate the equations in (a) and use conservation of charge to deduce thatΩ satisfies a homogeneous wave equation.

(d) Find initial conditions for the wave equation in (c) which guarantee that the Lorenz gauge condition is always satisfied and that E and B in (b) are the physical electric and magnetic fields.

1 C = jA - + Pot 2A at - 1 2 ( x A) 2 .