PHYS 2212 Module 12.3

Energy Carried by Electromagnetic Waves

Recommended Reading

12.3 Energy Carried by Electromagnetic Waves

Learning Objectives

By the end of this section, you will be able to:

  • Express the time-averaged energy density of electromagnetic waves in terms of their electric and magnetic field amplitudes
  • Calculate the Poynting vector and the energy intensity of electromagnetic waves
  • Explain how the energy of an electromagnetic wave depends on its amplitude, whereas the energy of a photon is proportional to its frequency

Energy in Electromagnetic Waves


Practice 12.3.1
In a sinusoidal, traveling electromagnetic wave in a vacuum, the magnetic energy density…
Check your answer: B. is maximum where the electric field has its greatest value.

Poynting Vector and Intensity of an Electromagnetic Wave

Practice 12.3.2
The drawing shows a sinusoidal electromagnetic wave in a vacuum at one instant of time at points between x = 0 and x = λ.

At this instant, at which of the values of x in the drawing does the instantaneous Poynting vector have its maximum magnitude?
Check your answer: D. x = 0, x = λ/2, and x = λ
Practice 12.3.3
A small source radiates an electromagnetic wave with a single frequency into vacuum, equally in all directions. As the wave propagates, its intensity:
Check your answer: B. decreases.
Practice 12.3.4
What is the average magnitude of the Poynting vector 13 km from a radio transmitter broadcasting isotropically (equally in all directions) with an average power of 200 kW?
Check your answer: E. 94 µW/m2


What is the approximate magnitude of the electric field on a page if you are reading a book outdoors under the shade of a tree and happen to leave the book on the ground where the Sun shines on it? The intensity of sunlight reaching the surface of the Earth is about 1000 W/m2.

A fusion reactor focuses 2×1013 watts of x-rays on this deuterium capsule for 5 nanoseconds.

(a) What is the average energy density of the radiation?

(b) What is the electric field amplitude of the radiation?