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

AI Thread Summary
The discussion focuses on calculating the energy transported by an electromagnetic (EM) wave with a given electric field strength. The rms strength of the E field is 36.5 mV/m, and the area in question is 1.15 cm². Participants clarify the use of the formula for energy density, ε₀E², and the conversion of units to ensure correct calculations. The correct approach involves multiplying the energy density by the area and the speed of light, followed by converting the result to joules per hour. The final calculations aim to resolve any discrepancies in the expected answer.
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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!
 
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Queue said:

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.
 
I think you did it correctly, but I'll just ask if you converted the area to m2 units
 
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!
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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