Consider a plane electromagnetic wave with a frequency, wo, propagating in vacuum in the 2 direction with its electric (a) write down the form for the electric field, magnetic field, vector potential, and scalar potential for this wave b) suppose the wave is a pulse with a well-defined beginning and end, that is, the vector potential has an "envelope" field polarized in the & direction. (should be easy). that is a function of z -ct (and the other fields have an appropriate form). does such a wave also satisfy c) consider an electron starting at rest that sits in the path of the electromagnetic wave. what are the equations (d) use the equations frorn part c) to show that the canonical momentunn in the direction and γ are maxwell's equations? of motion and the conservation of energy equation? (write out the equations for dp/dt and dy/dt.) constants of the motion. hint: for the second constant use a linear combination of the dr/dt and dp/dt equations. (e) if the electron starts at rest, then what is maximum kinetic energy as it oscillates in the wave? (f) what is its kinetic energy after the wave completely passes by it?