How much energy is transported by an EM wave with a given E field strength?

[Queue]

Homework Statement

How much energy is transported across a 1.15 cm^2 area per hour by an EM wave whose E field has an rms strength of 36.5 mV/m?

Homework Equations

E=hv?
The big problem I'm having is that I don't know what formulae to use.

The Attempt at a Solution

I know what V/m = J/C = J/(A*s) and I know I need to get to J/h. But I don't know what I have that would include Amps or Coloumbs to get rid of that part (I've resorted to trying to sort out units in the face of the lack of equations.

Thanks!

 

[Queue]

Homework Statement

How much energy is transported across a 1.15 cm^2 area per hour by an EM wave whose E field has an rms strength of 36.5 mV/m?

Homework Equations

E=hv?
The big problem I'm having is that I don't know what formulae to use.

The Attempt at a Solution

I know what V/m = J/C = J/(A*s) and I know I need to get to J/h. But I don't know what I have that would include Amps or Coloumbs to get rid of that part (I've resorted to trying to sort out units in the face of the lack of equations.

Thanks!

Ok, I have from my book (which was just returned to me) that energy in a wave is given by \epsilon_0 E² with units of J/m³. So I have u = 8.85*10^-12*(36.5*10^-3)². From there I divided by the area I am given (1.15 cm²) and then multiplied by the speed of light (in hours) to give me the right units but my answer was incorrect according to mastering physics. Perhaps I made a math error or perhaps I'm having conceptual issue. Any help would be appreciated.

 

[Redbelly98]

I think you did it correctly, but I'll just ask if you converted the area to m² units

 

[Queue]

I did convert to square meters.

I multiplied by area, didn't divide like I thought I was supposed to which actually makes my units work out.

This gives me u = $$\epsilon_0 E^2$$ = 8.85*10^-12*(3.65*10³)² J/(m³). From there I have u*A = 8.85*10^-12*(3.65*10³)²*0.000115 J/m. Then I multiplied by c giving u*A*c = 8.85*10^-12*(3.65*10³)²*0.000115*3*10⁹ = whatever it is J/s. Then I just multiplied by 3600 (seconds per hour) to get J/h.

Thanks!