2. In a certain 2D radiation problem (all fields independent of z), the only non-zero compo-...

 

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2. In a certain 2D radiation problem (all fields independent of z), the only non-zero compo- nents of fields are მს di H=2jweo; E= -x- +y ду дх The media constants are (eo, po). As usual the radian frequency is w. Let us expand the potential as (x, y) 1 2πT 1 + at the theo thuyết ch -∞< x < ∞, y ≥ 0. 88 If the r-component of electric field is given at y = 0+ to be E₂(x, 0): = Eo sin [k(-x)], -1/2 ≤x≤l/2, (i) Determine & by specializing the field expressions to y = 0. Evaluate the relevant integral in a closed form. (15 points) (ii) Find expressions for all components of fields for y≥ 0. (You may leave the field expressions in the form of integrals over kr.) (10 points) (iii) What is the expression for real part of power flow per unit width (in the z direction)? (Your answer can be left in terms of one integral.) (10 points) 2. In a certain 2D radiation problem (all fields independent of z), the only non-zero compo- nents of fields are მს di H=2jweo; E= -x- +y ду дх The media constants are (eo, po). As usual the radian frequency is w. Let us expand the potential as (x, y) 1 2πT 1 + at the theo thuyết ch -∞< x < ∞, y ≥ 0. 88 If the r-component of electric field is given at y = 0+ to be E₂(x, 0): = Eo sin [k(-x)], -1/2 ≤x≤l/2, (i) Determine & by specializing the field expressions to y = 0. Evaluate the relevant integral in a closed form. (15 points) (ii) Find expressions for all components of fields for y≥ 0. (You may leave the field expressions in the form of integrals over kr.) (10 points) (iii) What is the expression for real part of power flow per unit width (in the z direction)? (Your answer can be left in terms of one integral.) (10 points)

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Sure here are the solutions to the three parts of the problem i To determine u by specializing the f... View the full answer