Energy per unit area of EM wave

[x^2]

Homework Statement

The E field in an EM wave has a peak of 22.8 mV/m. What is the average rate at which this wave carries energy across unit area per unit time?

Homework Equations

S = e_0*c*E^2

The Attempt at a Solution

where e_0 = 8.85*10^-12
c = 3*10^8
E = 0.0228 V/m

S = (8.85E-12)*(3*10^8)*(0.0228)^2 = 1.38017E-6 W/m^2

Hello,

I trying finding the Poynting vector S using the equation e_0*c*E^2 as I have all the needed values. This produces an answer of 1.380E-6 W/m^2 which was incorrect. Where did I go wrong?

Thanks,
x^2

 

[x^2]

Got it... I have to divide the peak of the E field by Sqrt(2) to get the RMS or the average value so I can find the average energy.

Thanks for such a great resource!
x^2

 

[nlightner]

Dear x^2,

The equation you used, S = e_0*c*E^2, is the correct equation for calculating the Poynting vector, which represents the energy per unit time per unit area carried by an EM wave. However, the value you used for the electric field, 0.0228 V/m, is not the peak value as stated in the problem. The peak value is 22.8 mV/m, which is equal to 0.0228 V/m. Therefore, the correct calculation would be:

S = (8.85E-12)*(3*10^8)*(0.0228*10^-3)^2 = 1.380E-6 W/m^2

Note that in the calculation, the electric field value is converted to SI units (mV to V and m to m^-3). This small conversion factor may have been the reason for the incorrect answer. Always make sure to use the correct units in your calculations.

I hope this helps. Keep up the good work!

Best,