How Does Permittivity Affect Energy Transmission in EM Waves?

AI Thread Summary
The discussion centers on calculating the energy passing through a sphere in a nonmagnetic medium with a given permittivity and electric field amplitude. Two methods for calculating energy transmission are proposed: using the average power formula and integrating the Poynting vector over the sphere. The question of whether to replace the permittivity of free space with the medium's permittivity in calculations is raised. Clarification is provided that the sphere is simply a volume within a dielectric medium with ε=4. The conversation emphasizes the importance of integrating the Poynting vector for accurate energy transmission results.
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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