How Does Permittivity Affect Energy Transmission in EM Waves?

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Homework Help Overview

The discussion revolves around the impact of permittivity on energy transmission in electromagnetic (EM) waves, specifically in the context of a sphere placed in a nonmagnetic medium with a given permittivity and electric field amplitude. The original poster presents a problem involving energy passing through the surface of the sphere over a specified time period.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster considers two approaches to calculate energy transmission: one using a formula involving the average Poynting vector and another involving integration over the sphere. They question whether to replace the permittivity of free space with the given permittivity in their calculations. Additionally, they explore the implications of the sphere being in a nonmagnetic medium and its effect on the magnetic field.

Discussion Status

Some participants seek clarification on the nature of the sphere, specifically its material composition, while others suggest considering integration of the Poynting vector over the sphere's cross-section. The discussion is ongoing, with multiple interpretations and approaches being explored.

Contextual Notes

The problem context includes assumptions about the sphere being a spherical volume within a dielectric medium with a specified permittivity, and the implications of being in a nonmagnetic medium are under consideration.

diracdelta
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Homework Statement


Sphere of a radius R=50 cm is in nonmagnetic medium of
permittivity ε=4. EM wave with amplitude of electric field Em= 200 V/m is spreading through the medium.
How much energy pass through surface of sphere through 1 minute?

I have couple of question here. Since the sphere is in nonmagnetic medium how will that reflects of her magnetic field?
She doesn't have one?

So here's next flow of mind.I thought of two possibilities.
1) Sav*A*T= ε0*c*E*T
Q: Should i replace ε0 with ε?
Calculating this is quite easy, not sure if correct.

2)
Lets integrate over whole sphere of radius R, to find total Energy/time, that is, total power.
P = ∫sphere Savg
this way is much longer as far as mathemathics, but in the end, it should turn out same.

Are both solutions good?
 
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What is the sphere made of? Is it just a spherical volume within the e=4 dielectric, or metallic, or air, or ?
 
Its just spherical volume within e=4.
 
diracdelta said:
Its just spherical volume within e=4.
Consider integrating the poynting vector over the sphere's internal "great circle" cross-section.
 

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