Energy and Momentum of Electromagnetic Waves
Learn Energy Density, Momentum, Radiation Pressure, Photon Concepts, Poynting Vector and Advanced Numericals with complete derivations energy and momentum of em waves .
Section 2: Introduction
Electromagnetic waves are not only field oscillations; they are carriers of energy and momentum. When sunlight falls on a surface, it transfers energy and a tiny amount of momentum. This momentum transfer creates radiation pressure. The same idea explains why solar sails can be pushed by sunlight, why laser beams can exert force, and why electromagnetic waves are useful in space research.
Their electric and magnetic fields store and transport energy through space.
Momentum transfer produces force and pressure on surfaces.
A reflecting sail receives double momentum transfer, so sunlight can push it continuously.
Section 3: Energy Density of EM Waves
Electric Energy Density
uE = 12 ε0E2Electric field stores energy per unit volume.
Magnetic Energy Density
uB = B22μ0Magnetic field also stores energy per unit volume.
Derivation of uE = uB
E = cB c2 = 1μ0ε0 uE = 12 ε0E2 = 12 ε0c2B2 uE = B22μ0 = uB u = uE + uB = ε0E2Section 4: Poynting Vector
S→ = E→ × B→μ0The Poynting vector gives energy flow per unit area per unit time. It points in the direction of energy transport and is parallel to the propagation direction.
Section 5: Momentum of EM Waves
Electromagnetic waves carry momentum because they carry energy. Momentum transfer from light to matter creates radiation pressure.
From Einstein's photon energy-momentum relation for massless radiation, total energy is related to momentum by E = pc. Hence photons transfer momentum when absorbed or reflected.
Section 6: Radiation Pressure
Radiation pressure is force per unit area due to light or electromagnetic radiation.
Perfect Absorber
P = IcThe wave gives its forward momentum to the surface.
Perfect Reflector
P = 2IcMomentum reverses, so momentum transfer doubles.
| Surface | Pressure | Force on area A | Reason |
|---|---|---|---|
| Perfect absorber | I/c | IA/c | Momentum is absorbed. |
| Perfect reflector | 2I/c | 2IA/c | Momentum changes direction. |
Section 7: Applications
A large reflective sail gains momentum from sunlight and can move spacecraft without fuel.
Radiation pressure produces small but continuous forces on satellites.
High-intensity lasers can push small objects by momentum transfer.
Light pressure helps balance gravitational compression inside stars.
Sunlight and solar wind push dust and ions away from the Sun.
Focused lasers can trap and manipulate tiny particles.
Photon momentum is important in precision spacecraft navigation and solar sail missions.
Section 8: Important Mathematical Expressions
Section 9: Solved Numericals
Sections 10-14: PYQs and Exam Questions
Section 15: Case Study Questions
Section 16: Most Important Conceptual Questions
Section 17: One-Page Revision Sheet
Formula Summary
uE = ½ε0E², uB = B²/(2μ0)S = E × B/μ0, E = pcPabs = I/c, Pref = 2I/cKey Facts
EM waves carry energy, momentum and pressure. Reflection doubles momentum transfer. Poynting vector gives energy flow direction.
Exam Tricks
Convert cm² to m² before using force formulas. Use reflecting formula only for mirrors. Use E = pc for radiation momentum.
Memory Tips
Absorber: one momentum transfer. Reflector: two momentum transfers. Energy density: electric part equals magnetic part.
Section 18: Common Mistakes
Section 19: FAQ
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