How Do You Calculate Light Intensity in an Insulating Magnetic Material?

[sunmaggot]

Homework Statement

An electromagnetic wave with frequency 65.0Hz travels in an insulating magnetic material that has dielectric constant 3.64 and relative permeability 5.18 at this frequency. The electric field has amplitude 7.20×10−3V/m.

What is the intensity of the wave?

Homework Equations

I = S average = 1/2 ε₀ c E_max²

The Attempt at a Solution

the above equation is what I only have from my textbook, and it is for vacuum case. However, in the question, it has dielectric constant and relative permeability. I tried changing c into the light speed in the medium, not correct. I tried using equation from wiki, that is, times refractive index in the above equation, doesn't work. I tried simply ignore the refractive index problem, and doesn't work.

 

[Simon Bridge]

Please show your working.
How do you know "it didn't work"?

You book should have shown you a derivation for the formula it gave you... check that you are accounting for all the assumptions correctly.
Your book should include some text about how EM fields are different in a medium.
Have a go deriving the formula for intensity in a magnetic medium.

 

[forkinsocket]

Can someone help? I have literally the exact same question, which I already gave up on and have the answer for, but still don't understand.

My book says that the required modifications for the intensity in a medium are "simple." Replace $\epsilon_0$ with the permittivity $\epsilon$, replace $\mu_0$ with the permeability $\mu$, and replace $c$ with the speed $v$.

I replaced $\mu_0$ with the permeability given, and replaced $c$ with the speed found in a previous problem, and still got the problem completely wrong (by many orders of magnitude). I did:
$$(Emax * Bmax)/(2*5.18)$$ and $$(Emax ^2)/(2*5.18*v)$$ [all with the correct substitutions as found in previous problems] and both ended up with the same result, which was wrong.

 

[vielgluck]

If you use I = .5*sqrt( ε0/μ0)(Emax^2) and modify it with the dielectric constant and relative permittivity like so
I = .5*sqrt( ε0*3.64/(μ0*5.18))(Emax^2)