Energy per unit area of EM wave

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SUMMARY

The average rate at which an electromagnetic (EM) wave carries energy across unit area per unit time, known as the Poynting vector (S), can be calculated using the formula S = e_0 * c * E^2. In this discussion, the peak electric field (E) is given as 22.8 mV/m, leading to an initial calculation of S = 1.38017E-6 W/m^2. However, the correct approach requires dividing the peak E field by √2 to obtain the root mean square (RMS) value, which is essential for accurate energy calculations.

PREREQUISITES
  • Understanding of electromagnetic wave properties
  • Familiarity with the Poynting vector concept
  • Knowledge of the constants e_0 (permittivity of free space) and c (speed of light)
  • Basic proficiency in algebra for manipulating equations
NEXT STEPS
  • Learn about the derivation and applications of the Poynting vector in electromagnetic theory
  • Study the relationship between peak and RMS values in AC circuits
  • Explore the implications of energy density in electromagnetic waves
  • Investigate the role of permittivity and permeability in wave propagation
USEFUL FOR

Students studying electromagnetism, physicists analyzing wave properties, and engineers working with electromagnetic field applications.

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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,
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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!
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