Plane Waves David Sutrisno Dodi Fikri Enggou Prastyo Galih Ilham

5.1 General Wave Equation We’ll consider that medium is free of any charge : Material media that are linear, isotropic, homogeneous and time invariant.

Maxwell’s equation in the point form Gauss’s law : Gauss’s law for magnetic fields: Faraday’s law : Ampere’s circuital law: Constitutive relations:

This is the Helmholtz wave equation for E

Time harmonic wave equation Persamaan Helmholtz untuk time- harmonic fields, time derivative menjadi, sehingga :

Persamaan gelombang Helmholtz umumnya ditulis dalam bentuk : ….(a) Dimana gamma adalah konstanta propagasi yang didefinisikan sebagai berikut : Gamma is equal to a real part (the attenuation, alpha, in nepers per meter) and an imaginary part (the phase constant, or beta, in radians per meter). …… (b)

Persamaan (a) adalah persamaan Helmholtz untuk time- harmonic medan listrik. Untuk time-harmonic medan magnet persamaannya :

Intrinsic impedance n (eta) Merupakan perbandingan antara dan Inserting the expression for gamma from (b), we find

Examples 5.1 Given material with, and and an a wave with f = 1.00 GHz, we want to find

Propagating Field Relation Example 5.2 Consider the case where And we want to find H.

5.2 PROPAGATION IN LOSSLESS, CHARGE FREE MEDIA

5.3 PROPAGATION IN DIELECTRICS

Permitivitas kompleks

Loss Tangent

Low loss dielectrics

Tabel parameter bahan dielektrik Copper10 Seawater47212 Glass100.01

Contoh soal In a media with properties s = S/m, e r = 1.0, m r = 100., and f = 100. MHz, a 1.0 mA/m amplitude magnetic field travels in the +x direction with its field vector in the z direction. Find the instantaneous form of the related electric field intensity.

Propagation In Conductors S.402 | Tuesday, 4 April 2011

Propagation In Conductors Since for good conductor, the interior bracketed term can be written: And the expressions for α and β are then shown to be equal:

The intrinsic impedance is approximated by: Since. We can rearrange this equation by considering Leading to

Can also be written: A consequence ol the large σ is the decrease in the propagation velocity and wavelength. We have: And since

Current in Conductors The resistor for such a slab is The amplitude decreases as The corresponding current density by Ohm’s law is

To calculate the current through a surface extending from 0 to infinity in the z direction and of width w in the y direction. We integrate, then we have: We can use this expression and the one for current to find the R for length L of slab of width, that extwnds from z=0 to infinity. We have

Or Where Changing the limits on our integration for the current:

Then easy to show that the skin effect resintance can be written: Skin effect for cylindrical (wire or pipe)

P5.20: Calculate the skin depth at 1.00 GHz for (a) copper, (b) silver, (c) gold, and (d) nickel.