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Problem 3 Consider a possible solution to Maxwell's equations in vacuum given by A(x, t) = Ao exp(i(kx - wt)), V(x, t) = 0 where A is the vector potential and V is the scalar potential. Suppose Ao, k and w are constants in space and time. a) Compute the time-dependent electric and magnetic fields from the given potentials. Show your work. b) Give the contraints, if any, on Ao, k and w imposed by the following two Maxwell's equations in vacuum (show your work): (i) V.E=0 (ii) DXE - OB Give a physical interpretation of each of the constraints. (If you could not solve part a), then use expression for a planar electromagnetic wave propagating in y-direction in part b).).
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