1 / 33

Chapter 24

Chapter 24. Electromagnetic Waves. Unpolarized visible light. X-ray. Radio waves. Polarized visible light. 24.1 Electromagnetic Waves, Introduction. Electromagnetic (EM) waves permeate our environment EM waves can propagate through a vacuum

lerato
Download Presentation

Chapter 24

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 24 Electromagnetic Waves

  2. Unpolarized visible light X-ray Radio waves Polarized visible light

  3. 24.1 Electromagnetic Waves, Introduction • Electromagnetic (EM) waves permeate our environment • EM waves can propagate through a vacuum • Much of the behavior of mechanical wave models is similar for EM waves • Maxwell’s equations form the basis of all electromagnetic phenomena

  4. Conduction Current • A conduction current is carried by charged particles in a wire • The magnetic field associated with this current can be calculated by using Ampère’s Law: • The line integral is over any closed path through which the conduction current passes

  5. Conduction Current, cont. • Ampère’s Law in this form is valid only if the conduction current is continuous in space • In the example, the conduction current passes through only S1 but not S2 • This leads to a contradiction in Ampère’s Law which needs to be resolved

  6. James Clerk Maxwell • 1831 – 1879 • Developed the electromagnetic theory of light • Developed the kinetic theory of gases • Explained the nature of color vision • Explained the nature of Saturn’s rings

  7. Displacement Current • Maxwell proposed the resolution to the previous problem by introducing an additional term called the displacement current • The displacement current is defined as

  8. Displacement current • The electric flux through S2 is EA • S2 is the gray circle • A is the area of the capacitor plates • E is the electric field between the plates • If q is the charge on the plates, then Id = dq/dt • This is equal to the conduction current through S1

  9. Displacement Current • The changing electric field may be considered as equivalent to a current • For example, between the plates of a capacitor • This current can be considered as the continuation of the conduction current in a wire • This term is added to the current term in Ampère’s Law

  10. Ampère-Maxwell Law • The general form of Ampère’s Law is also called the Ampère-Maxwell Law and states: • Magnetic fields are produced by both conduction currents and changing electric fields

  11. 24.2 Maxwell’s Equations, Introduction • In 1865, James Clerk Maxwell provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena • Maxwell’s equations also predicted the existence of electromagnetic waves that propagate through space • Einstein showed these equations are in agreement with the special theory of relativity

  12. Maxwell’s Equations Gauss’ Law (electric flux) Gauss’ Law for magnetism Faraday’s Law of induction Ampère-Maxwell Law The equations are for free space No dielectric or magnetic material is present

  13. Lorentz Force • Once the electric and magnetic fields are known at some point in space, the force of those fields on a particle of charge q can be calculated: • The force is called the Lorentz force

  14. 24.3 Electromagnetic Waves • In empty space, q = 0 and I = 0 • Maxwell predicted the existence of electromagnetic waves • The electromagnetic waves consist of oscillating electric and magnetic fields • The changing fields induce each other which maintains the propagation of the wave • A changing electric field induces a magnetic field • A changing magnetic field induces an electric field

  15. Plane EM Waves • We assume that the vectors for the electric and magnetic fields in an EM wave have a specific space-time behavior that is consistent with Maxwell’s equations • Assume an EM wave that travels in the x direction with the electric field in the y direction and the magnetic field in the z direction

  16. Plane EM Waves, cont • The x-direction is the direction of propagation • Waves in which the electric and magnetic fields are restricted to being parallel to a pair of perpendicular axes are said to be linearly polarized waves • We assume that at any point in space, the magnitudes E and B of the fields depend upon x and t only

  17. Equations of the Linear EM Wave • From Maxwell’s equations applied to empty space, E and B are satisfied by the following equations • These are in the form of a general wave equation, with • Substituting the values for mo and eo gives c = 2.99792 x 108 m/s

  18. Solutions of the EM wave equations • The simplest solution to the partial differential equations is a sinusoidal wave: • E = Emax cos (kx – wt) • B = Bmax cos (kx – wt) • The angular wave number is k = 2 p / l • l is the wavelength • The angular frequency is w = 2 p ƒ • ƒ is the wave frequency

  19. Ratio of E to B • The speed of the electromagnetic wave is • Taking partial derivations also gives

  20. Properties of EM Waves • The solutions of Maxwell’s are wave-like, with both E and B satisfying a wave equation • Electromagnetic waves travel at the speed of light • This comes from the solution of Maxwell’s equations

  21. Properties of EM Waves, 2 • The components of the electric and magnetic fields of plane electromagnetic waves are perpendicular to each other and perpendicular to the direction of propagation • The electromagnetic waves are transverse waves

  22. Properties of EM Waves, 3 • The magnitudes of the fields in empty space are related by the expression • This also comes from the solution of the partial differentials obtained from Maxwell’s Equations • Electromagnetic waves obey the superposition principle

  23. EM Wave Representation • This is a pictorial representation, at one instant, of a sinusoidal, linearly polarized plane wave moving in the x direction • E and B vary sinusoidally with x

  24. Rays • A ray is a line along which the wave travels • All the rays for the type of linearly polarized waves that have been discussed are parallel • The collection of waves is called a plane wave • A surface connecting points of equal phase on all waves, called the wave front, is a geometric plane

  25. Doppler Effect for Light • Light exhibits a Doppler effect • Remember, the Doppler effect is an apparent change in frequency due to the motion of an observer or the source • Since there is no medium required for light waves, only the relative speed, v, between the source and the observer can be identified

  26. Doppler Effect, cont. • The equation also depends on the laws of relativity • v is the relative speed between the source and the observer • c is the speed of light • ƒ’ is the apparent frequency of the light seen by the observer • ƒ is the frequency emitted by the source

  27. Doppler Effect, final • For galaxies receding from the Earth, v is entered as a negative number • Therefore, ƒ’<ƒ and the apparent wavelength, l’, is greater than the actual wavelength • The light is shifted toward the red end of the spectrum • This is what is observed in the red shift

More Related