How does a charge q oscillating at a certain frequency produce electromagnetic waves? Sketch a schematic diagram depicting the electric and magnetic fields for an electromagnetic wave propagating along the Z-direction.
Solution
An oscillating charge is an accelerating charge. Its oscillation produces an electric field that varies with time; by the Ampere--Maxwell law this changing electric field produces a time-varying magnetic field, which in turn (by Faraday's law) regenerates a changing electric field. This mutual, in-phase regeneration of E and B travels outward as an electromagnetic wave whose frequency equals the frequency of oscillation of the charge. For propagation along z, the sketch shows Ex=E0sin(kz−ωt) and By=B0sin(kz−ωt), mutually perpendicular and both perpendicular to z.
