Chapter 34 Electromagnetic Waves and light

Electromagnetic waves in our life Microwave oven, EM wave is used to deliver energy. Radio/TV, cell phones, EM wave is used to carry information. Telephone and internet: electrical signal in copper wires is NOT EM wave, but fiber optics is the backbone of the network. The wireless connection for your laptop, the bluetooth headset for your iPod, … Without EM wave, there would be no life on Earth. – why?

Plane EM waves, the simplest form A review: a wave is a disturbance that propagates through space and time, usually with transference of energy PLAY ACTIVE FIGURE An EM wave is the oscillation between electric and magnetic fields. The electric field oscillates in the x-y plane, along the y direction; the magnetic field oscillates in the x-z plane and along the z direction. The EM wave propagates along the x axis, with the speed of light c, in vacuum.

Wave propagation A sinusoidal EM wave moves in the x direction with the speed of light c, in vacuum. PLAY ACTIVE FIGURE The electric field direction (here the y axis direction) is called the polarization direction. When this polarization direction does not change with time, it is said that the EM wave is linearly polarized. Another common polarization is the circular polarization, when the electric field direction moves in a circle The magnitudes E and B of the fields depend upon x (the location in the wave) and t (time) only: Here k is the wave number.

Rays, wave front and plane wave A ray is a line along which the wave travels. In a homogeneous medium for EM waves (vacuum being one), rays follow straight lines. The surface that connects points of equal phase in a group of rays (waves) is called the wave front. When this wave front is a geometric plane, this collection of waves is called a plane wave.

Maxwell’s equations of EM waves Gauss’s Law of electric field: Gauss’s Law of magnetic field: Here the emf is actually distributed over the conducting ring. From the definition of potential, we know that the emf here equals: Faraday’s Law of induction: So Faraday’s Law of induction now reads:

Maxwell’s modification to Ampere’s Law Ampere’s Law of magnetic field: Here the current flows in a wire. Now let’s examine the case when there is a capacitor in the current path: Ampere’s Law applies to the wire part. The current flows into the upper plate of the capacitor, flows out from the lower plate, creating charge accumulation in the capacitor and build up the electric field. Constructing a Gaussian surface which has two parts: S 1 and S 2.

Maxwell’s modification to Ampere’s Law Gauss’ Law says that: So one has: Here I d is called the displacement current. With it, the Ampere’s Law is now completed as: It is often called Ampere-Maxwell Law

Maxwell’s equations of EM waves Gauss’s Law of electric field: Gauss’s Law of magnetic field: Faraday’s Law of induction: Ampere-Maxwell Law: These four equations are called Maxwell’s Equations. These are the integral forms. The differential forms are: With Lorenz force Law, we complete the laws of classical electromagnetism.

James Clerk Maxwell 1831 – 1879 Scottish physicist Provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena His equations predict the existence of electromagnetic waves that propagate through space His equations unified the electric and magnetic fields, and provide foundations to many modern scientific studies and applications.

Energy in EM waves From Maxwell’s equations, one can prove: The speed of light is The electric field to magnetic field ratio is The energy flow in an EM wave is described by the Poynting vector The wave energy intensity is The energy density is

Producing EM waves through an antenna Use a half-wave antenna as an example Two conducting rods are connected to a source of alternating voltage The length of each rod is one-quarter of the wavelength of the radiation to be emitted The oscillator forces the charges to accelerate between the two rods The antenna can be approximated by an oscillating electric dipole The magnetic field lines form concentric circles around the antenna and are perpendicular to the electric field lines at all points The electric and magnetic fields are 90 o out of phase at all times This dipole energy dies out quickly as you move away from the antenna

The EM wave Spectrum Radio waves Microwaves Infrared Ultraviolet, UV Visible light Gamma and X rays

Notes on the EM wave Spectrum Radio Waves Wavelengths of more than 10 4 m to about 0.1 m Used in radio and television communication systems Microwaves Wavelengths from about 0.3 m to m Well suited for radar systems Microwave ovens are an application Infrared waves Wavelengths of about m to 7 x m Incorrectly called “heat waves” Produced by hot objects and molecules Readily absorbed by most materials Visible light Part of the spectrum detected by the human eye Most sensitive at about 5.5 x m (yellow- green) Ultraviolet, X-rays and Gamma rays

More About Visible Light Different frequencies (or wavelengths in vacuum) correspond to different colors The range of wavelength in vacuum is from red ( λ ~ 7 x m) to violet (λ ~4 x m)

More notes on the EM wave Spectrum Ultraviolet light Covers about 4 x m to 6 x m Sun is an important source of uv light Most uv light from the sun is absorbed in the stratosphere by ozone X-rays Wavelengths of about m to m Most common source is acceleration of high- energy electrons striking a metal target Used as a diagnostic tool in medicine

Gamma rays Wavelengths of about m to m Emitted by radioactive nuclei Highly penetrating and cause serious damage when absorbed by living tissue Looking at objects in different portions of the spectrum can produce different information More notes on the EM wave Spectrum

Wavelengths and Information These are images of the Crab Nebula They are (clockwise from upper left) taken with x-rays visible light radio waves infrared waves