Solve Media Homework: Relative Permittivity of Non-dissipative Medium

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In summary, we have a problem involving a uniform plane wave propagating in a non-dissipative medium with a frequency of 20 MHz. Two probes located at different positions measure phase angles of 98 degrees and -15 degrees. Using the equations k = w*sqrt(u*e) and Phase angle = kz, we can solve for the relative permittivity (e/e0) of the medium to be approximately 2.83 * 10^-9 F/m. The other probe located at z = 0 would have the same relative permittivity, as there is only one epsilon value for the medium.
  • #1
Maat
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Homework Statement



A uniform plane wave propagates in a non-dissipative medium in the positive z direction. The frequency of the wave is 20 MHz. A probe located at z = 0 measures the phase of the wave to be 98 degrees. An identical probe located at z = 2 m measures the phase to be -15 degrees. What is the relative permittivity (e/e0) of the medium.

Homework Equations



k = w*sqrt(u*e)

w = 2*pi*f

wt - kz = a constant

w is angle velocity, u is permeability, e is permittivity

The Attempt at a Solution



wt = phase angle

Phase angle = kz

K2 = -15/2 = -7.5

w = 2*pi*(20*10^6)

K2 = w*sqrt(u*e), solve for e (e2)

e2 = 2.83 * 10^-9 F/m

Now I'm stuck on how to get the other e since z = 0. I think this problem should be easy, but I'm not seeing something.
 
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  • #2
Why is your topic "conducting" media? It's not conducting. Conducting media dissipate. Yours is stated to be "non-dissipative".

Maat said:

Homework Statement



k = w*sqrt(u*e)
Phase angle = kz
w = 2*pi*(20*10^6)

All correct. (Some of the other stuff you posted wasn't, but never mind).

So how about equating delta degrees to delta kz?
 
  • #3
If I equated the deltas, how would I get two different e's? My thought was to get two different k's and from that find the two e's to compare.
 
  • #4
Maat said:
If I equated the deltas, how would I get two different e's? My thought was to get two different k's and from that find the two e's to compare.

Why are you looking for two different epsilons? there is only one epsilon.
There is also only one k.
There are however two z's and two phase angles.
 
  • #5
Ah is that because the other epsilon is just e0?
 
  • #6
Ok I see now. Thank you very much.
 

FAQ: Solve Media Homework: Relative Permittivity of Non-dissipative Medium

1. What is the relative permittivity of a non-dissipative medium?

The relative permittivity of a non-dissipative medium, also known as the dielectric constant, is a measure of how much the electric field within the medium is reduced compared to the electric field in a vacuum.

2. How is relative permittivity different from absolute permittivity?

Relative permittivity is a dimensionless quantity that compares the electric field in a medium to the electric field in a vacuum, while absolute permittivity is a measure of the amount of charge that can be stored in a medium under a given electric field.

3. What factors affect the relative permittivity of a non-dissipative medium?

The relative permittivity of a non-dissipative medium is affected by the properties of the medium, such as its molecular structure, temperature, and pressure. It can also be influenced by the frequency and strength of the applied electric field.

4. How is the relative permittivity of a non-dissipative medium measured?

The relative permittivity of a non-dissipative medium is typically measured using a device called a capacitance meter. This instrument measures the capacitance of a capacitor filled with the medium in question, and then calculates the relative permittivity using the known capacitance of the vacuum.

5. What are some real-life applications of understanding relative permittivity of non-dissipative mediums?

Knowledge of relative permittivity is crucial in many fields, such as electrical engineering, telecommunications, and materials science. It is used to design and optimize electronic devices, calculate the capacitance of capacitors, and understand the behavior of electromagnetic waves in various materials.

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