Calculating Energy Transported by an EM Wave with a 36.5 mV/m E Field

[Queue]

Homework Statement

How much energy is transported across a 1.15 cm² area per hour by an EM wave whose E field has an rms strength of 36.5 mV/m?

Homework Equations

u (energy per unit volume) = $$\epsilon_0 E^2 \frac{J}{m^3}$$

The Attempt at a Solution

Since I have u = 8.85*10^-12*(36.5*10^-3)² J/(m^3). I multiply this by the given area (1.15 cm²) which gave me units of J/m. The only other thing that seems to make any sense that would get me to J/h would be to multiply by the speed of light in meters per hour.

 

[lanedance]

Hi Queue, that sounds reasonable to me - multiplying by the speed of light gives the power crossing the surface area. Transferring the speed to m/hr is equivalent to finding the power transfer in J/s, using m/s, then multiplying by 3600s to find the total energy trasnferred in an hour

 

[nlightner]

My response:

Calculating the energy transported by an EM wave requires understanding the energy density of the wave, which is given by the equation u = ε0E^2, where ε0 is the permittivity of free space and E is the electric field strength. In this case, the given E field has an rms strength of 36.5 mV/m. To find the energy transported across a given area, we can use the equation E = uA, where A is the area and E is the energy transported per unit time. In this case, the given area is 1.15 cm^2, or 0.000115 m^2. Plugging in the values, we get E = (8.85*10^-12)*(36.5*10^-3)^2 * 0.000115 = 3.72*10^-16 J/h. This is the energy transported across the given area per hour. To convert this to J/m^2, we can multiply by the speed of light in meters per hour, which is approximately 1.08*10^10 m/h. Therefore, the energy transported across 1.15 cm^2 per hour is approximately 4.02*10^-6 J/m^2.