Normal incidence on dielectric and perfect conducting interfaces.

$($b$)$Given a AC current sheet, that is backed by a piece of semi infinite dielectric. Write the phasor expressions for the electric and magnetic fields that are associated with these electromagnetic waves that are created by the current sheet. Show all steps and provide explanation.

$($c$)$Instead of a semi infinite dielectric, a perfect dielectric is placed at the back. What should the thickness of the dielectric be such that the current sheet is located at the maximum of the electric field for the standing wave pattern in the dielectric $($hint: choose the thickness of the dielectric such that the current sheet is at the point of the maximum of the electric field$).$Show all steps and explain your reasoning.