A TEM wave (Ex, By) propagates in a linear, inhomogeneous material with a permittiv- ity (z) and a permeability μ(z). That is, the permittivity and permeability vary with position. Using Maxwell's Equations, show that Ex and B₁ can be written as the following sepa- rate, second-order, partial differential equations: J² Ex Ət² J² By Ət² = = 1 მ 1 дет €(z) Əzµ(z) Əz მ 1 მ J= [(2) Oz [m(s) Br]] მ Əz e(z) Əz

A TEM wave (Ex, By) propagates in a linear, inhomogeneous material with a permittiv- ity (z) and a permeability μ(z). That is, the permittivity and permeability vary with position. Using Maxwell's Equations, show that Ex and B₁ can be written as the following sepa- rate, second-order, partial differential equations: J² Ex Ət² J² By Ət² = = 1 მ 1 дет €(z) Əzµ(z) Əz მ 1 მ J= [(2) Oz [m(s) Br]] მ Əz e(z) Əz