How Does Permittivity Affect Energy Transmission in EM Waves?

[diracdelta]

Homework Statement

Sphere of a radius R=50 cm is in nonmagnetic medium of
permittivity ε=4. EM wave with amplitude of electric field E_m= 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) S_av*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 S_avg
this way is much longer as far as mathemathics, but in the end, it should turn out same.

Are both solutions good?

 

[rude man]

What is the sphere made of? Is it just a spherical volume within the e=4 dielectric, or metallic, or air, or ?

 

[diracdelta]

Its just spherical volume within e=4.

 

[rude man]

Its just spherical volume within e=4.

Consider integrating the poynting vector over the sphere's internal "great circle" cross-section.

 

[HalfLostAndSearching]

Both solutions are valid approaches to calculating the energy passing through the surface of the sphere in one minute. However, the first solution using the equation Sav*A*T= ε0*c*E*T is the more straightforward and efficient method. This equation takes into account the permittivity of the medium, which is necessary for accurately calculating the energy passing through the surface. In this case, you would use the value of ε (4) instead of ε0 in the equation.