A large, flat sheet carries a uniformly distributed electric current with current per unit width Js. This current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude
B = (1/2)μ0Js.
If the current is in the y direction and oscillates in time according to
Jmax (cos ωt) = Jmax[cos (−ωt)]
the sheet radiates an electromagnetic wave. The figure below shows such a wave emitted from one point on the sheet chosen to be the origin. Such electromagnetic waves are emitted from all points on the sheet. The magnetic field of the wave to the right of the sheet is described by the wave function
(1/2)μ0Jmax[sin (kx − ωt)].
(a) Find the wave function for the electric field of the wave to the right of the sheet. (Use the following as necessary: μ0, c for the speed of light, Jmax, k, x, ω, and t.) =