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6.10. For the TM modes (H, = 0) in rect- angular coordinates, with z variations...

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6.10. For the TM modes (H, = 0) in rect- angular coordinates, with z variations of the form e Bzz, derive expressions for the E- and H-field rectangular components in terms of E, =f(x)g (v)e-iBzz, where V Ez(x,y,z) + B-Ez(x, y, z) = 0. In other words, instead of expressing the electric and magnetic field components for TM modes (H, = 0) in terms of Az [as is done in 6- 59)), this time you start with Ez not being equal to zero and express all the electric and magnetic field components, except Ez in terms of Ez. This is an alternate way of finding the TM modes. Simplify the expres- sions. They should be in a form similar to those of (6-59). Hint: You should use Maxwell's equations back and forth. TM Rectangular Coordinate System ?, , - ; 1 H, = x 97 1 32, =- ' y 97. 1 7 32 = -i -IA 5 +B . dy 1 A, (6-59) H, = 0 3-2 +

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