Question

A uniform current J1 = Jocoswtêy flow on the surface z =0,and a second sheet of current J2 = J0sinwtêy flows in the surface z = pic/2w where ey is the unit vector along y and Jo,w are constant.

 a) Find solution of Maxwell's equations that fit the boundary conditions with E= B=0 z<0

 b) Calculate the flux of the poynting vector field and compare it to average power per unit area that must be supplied to drive these currents.

Answer 1

Given,

Unit current $J_1=J_o\cos\omega t\hat{e_y}$ current through z =0

And $J_2=J_o\cos\omega t\hat{e_y}$ and $z=\frac{\pi c}{2\omega}$

For the Maxwell's equation, for the boundary condition,

$\oint_c H.dl=\int \int_s(J_1.+\frac{\partial D}{\partial t})dS$

$J_{tot}=J+j \omega D$

$=j\omega c(\omega)E$