# Uniform plane wave parallel/perpendicular phasor problem

• asdf12312
In summary, the conversation discusses a problem involving calculating the components of an electric field using various equations. The equations used include lambda= 2*pi / k, Ei(z), Ei_perpendicular (z), Ei_parallel(z) eq., epsilon_r1=1, epsilon_r2=2.25, and eta_1=120*pi, eta_2=80*pi. The individual is having trouble understanding some parts of the problem and provides their attempt at a solution, including calculations and a diagram. They also ask for clarification on the equations for parallel/perpendicular Ei(z) field and how to use the formula for epsilon_r2 to find Ez(amplitude) for a specific part of the problem.
asdf12312

## Homework Equations

lambda= 2*pi / k
Ei(z), Ei_perpendicular (z), Ei_parallel(z) eq.
epsilon_r1=1, epsilon_r2=2.25
eta_1=120*pi, eta_2=80*pi

## The Attempt at a Solution

I having trouble understanding some parts of this problem. i get k1=3.61, k2=5.42 and for d) theta_i=tan-1(2/3)=33.7deg. the only way I could try to find the z-component Ez by using the parallel component of Ei(z), so it would be 9*x - Ez*z * e^-j(k1*sin(theta_i)*x + k1*cos(theta_i)*z) and I tried to draw a picture of this on xyz plane and I got tan(90-theta_i)=Ex/Ez and solving I get Ez (amplitude)=6, but not sure if I did that right.

My other problem with the equations for parallel/perpendicular Ei(z) field, the amplitude for perpendicular I get on y-plane or -4*y, for the amplitude on parallel the equation given as (x*cos(theta_i) - z*sin(theta_i)) * E(parallel) so would it be x*9*cos(theta_i) - z*6*sin(theta_i) for the parallel Ei field or am I understanding it wrong?

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Also, how can I use the formula for epsilon_r2 to find Ez(amplitude) for part c)? Any help would be appreciated, thank you.

## 1. What is a uniform plane wave?

A uniform plane wave is a type of electromagnetic wave that has a constant amplitude and phase throughout its entire extent. It is characterized by a constant direction of propagation and a uniform electric and magnetic field that are perpendicular to each other and to the direction of propagation.

## 2. What does it mean for a wave to be parallel or perpendicular?

The terms "parallel" and "perpendicular" refer to the orientation of the electric and magnetic fields in a uniform plane wave. In a parallel wave, the electric and magnetic fields are parallel to each other, while in a perpendicular wave, the electric and magnetic fields are perpendicular to each other.

## 3. What is a phasor in the context of a uniform plane wave?

A phasor is a mathematical tool used to represent the amplitude and phase of a sinusoidal wave. In the context of a uniform plane wave, a phasor can be used to describe the electric and magnetic fields at any point in the wave.

## 4. How do you solve a parallel/perpendicular phasor problem?

To solve a parallel/perpendicular phasor problem, you must first determine the direction of the electric and magnetic fields in the wave. Then, using the appropriate equations, you can calculate the amplitude and phase of the fields at a given point in the wave.

## 5. What are some practical applications of uniform plane waves?

Uniform plane waves have many practical applications, including in wireless communication, radar systems, and medical imaging. They are also used in research and development of new technologies, such as metamaterials and photonics.

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