Additional material for Tutorial 5# (part II- plane wave)

y

x

z

The instantaneous expression for the magnetic field intensity of a uniform plane wave propagating in the +y direction in air is given by Determine k0 and the location where Hz–field vanishes at t=3 ms.

Plane-wave: Example 1

y

x

z

6 70

ˆ 4 10 cos 10 / 4 ( / )zH a t k y A m

Plane-wave: Example 1

The E-field of a uniform plane wave propagating in a dielectric medium is given by 1) Determine the frequency and wavelength of

the wave; 2) What is the dialectic constant of the

medium? 3) Find the corresponding H-field.

8 8ˆ ˆ( , ) 2cos(10 / 3) (10 / 3) ( / )sinE t z x t z y t z V m

Plane-wave: Example 2

Plane-wave: Example 2

A 10-MHz uniform plane wave is traveling in a nonmagnetic medium with µ = µ 0 and εr = 9. Find (a) the phase velocity, (b) the wave number, (c) the wavelength in the medium, and (d) the intrinsic impedance of the medium.

Plane-wave: Example 3

A 60-MHz plane wave traveling in the –x direction in dry soil with relative permittivity εr = 4 has an electric field polarized along the z-direction. Assuming dry soil to be approximately lossless, and given that the magnetic field has a peak value of 10 (mA/m) and that its value was measured to be 7 (mA/m) at t = 0 and x = -0.75 m, develop complete expressions for the wave’s electric and magnetic fields.

Plane-wave: Example 4

Plane-wave: Example 4

Note that H is also perpendicular to k and also perpendicular to E. This can be established from the expression for H.

E

H

Direction of propagation

Note that:

knHE ˆˆˆˆ or E and H lie on the plane of constant phase (k·r = const)

Plane-wave: Example 4

Plane-wave: Example 4