Electromagnetic Energy and Momentum
Electromagnetic fields carry energy and momentum, transported by the Poynting vector and balanced through the Maxwell stress tensor.
Definition
The study of how the electromagnetic field stores and transports energy and momentum, expressed through the field energy density, the Poynting vector giving the energy flux, and the Maxwell stress tensor giving the momentum flux, all linked by local conservation laws.
Scope
This topic develops the conservation laws of electrodynamics: Poynting's theorem for energy flow, the electromagnetic energy density, the Poynting vector for energy flux, field momentum and the Maxwell stress tensor for momentum flow, and radiation pressure. It shows how charges and fields exchange energy and momentum while the total is conserved.
Core questions
- How much energy and momentum does an electromagnetic field carry?
- How is energy transported through a field according to Poynting's theorem?
- How do fields exert pressure and transfer momentum to matter?
Key concepts
- energy density
- Poynting vector
- Poynting's theorem
- field momentum
- Maxwell stress tensor
- radiation pressure
- conservation laws
Key theories
- Poynting's theorem
- The rate of change of field energy in a volume plus the energy flux out through its surface equals minus the work done on charges, with the Poynting vector giving the directional energy flow.
- Field momentum and the Maxwell stress tensor
- Electromagnetic fields carry momentum proportional to the Poynting vector, and the Maxwell stress tensor describes the flow of that momentum, accounting for forces such as radiation pressure.
Clinical relevance
Energy and momentum transport explain power flow in transmission lines and waveguides, radiation pressure used in optical tweezers and solar sails, and the heating effects exploited in radiofrequency and microwave therapy.
History
Poynting formulated the theorem on energy flow in the electromagnetic field in 1884, building on Maxwell's stress concepts. The associated radiation pressure was measured experimentally by Lebedev around 1900 and independently by Nichols and Hull, confirming that fields carry momentum.
Key figures
- John Henry Poynting
- James Clerk Maxwell
- Pyotr Lebedev
Related topics
Seminal works
- poynting1884
- jackson1998
Frequently asked questions
- What does the Poynting vector represent?
- It gives the magnitude and direction of the flow of electromagnetic energy per unit area per unit time, so its surface integral is the power crossing that surface.
- Do electromagnetic fields carry momentum?
- Yes; fields store momentum proportional to the Poynting vector, which is why light exerts radiation pressure and momentum is conserved overall when fields interact with matter.