Momentum density vector of a plane em wave

Click For Summary
SUMMARY

The magnitude of the momentum density vector of a plane electromagnetic wave in vacuum is equal to the energy density divided by the speed of light, c. This relationship is derived from the equation for the Poynting vector, \vec{S} = \vec{E} \times \vec{H}, which describes the energy flow per unit area. Understanding the momentum density vector is crucial for upper division physics courses, particularly in electromagnetism and wave mechanics.

PREREQUISITES
  • Understanding of electromagnetic waves
  • Familiarity with the Poynting vector
  • Basic knowledge of energy-momentum tensor
  • Concept of energy density in electromagnetic fields
NEXT STEPS
  • Study the derivation of the Poynting vector in detail
  • Learn about the energy-momentum tensor components in electromagnetism
  • Explore the relationship between energy density and momentum density in electromagnetic waves
  • Investigate applications of momentum density in wave mechanics
USEFUL FOR

Students in upper division physics courses, particularly those studying electromagnetism, wave mechanics, and anyone interested in the properties of electromagnetic waves.

aftershock
Messages
106
Reaction score
0

Homework Statement



Show that in vacuum the magnitude of the momentum density
vector of a plane electromagnetic wave is equal to the energy density
divided by the speed of light, c.

Homework Equations



[itex]\vec{S}[/itex] = [itex]\vec{E}[/itex]x[itex]\vec{H}[/itex]

The Attempt at a Solution



This doesn't seem too hard if you know what a momentum density vector is, so if this should be in the introductory section I apologize but it is a homework question from an upper division course.

The only thing I'm really looking for is how to find/ what is a momentum density vector. I have no idea how to go about finding it.
 
Physics news on Phys.org
Do you know how the 16 components of the energy-momentum tensor look like ?
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
Replies
5
Views
3K
Replies
2
Views
2K
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 6 ·
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 18 ·
Replies
18
Views
1K