Chapter 22 - Electromagnetic Waves

waves can be either

transverse or longitudinal depending on how the medium vibrates

if the vibrations are parallel to the direction of travel, the wave is

longitudinal

if the vibrations are perpendicular to the direction of travel, the

wave is transverse

waves repeat in

space and time

wavelength characterizes the

distance over which the wave repeats in space, and is related to the wave number (k)

period (T) characterizes the

duration over which the wave repeats in time, and is related to both frequency (f) and angular frequency 

the simple type of wave is a sinusoidal wave, known as a

plane wave 

plane wave - the first between the first two terms depends on the direction the wave is traveling → for a wave traveling in the positive x direction, 

it’s the minus sign 

plane wave - the first between the first two terms depends on the direction the wave is traveling → for a wave traveling in the negative x direction, 

it’s the plus sign 

gauss’s law relates electric field to

charge

gauss’s law for magnetic field:

no magnetic monopoles 

an electric field is produced by a 

changing magnetic field (faraday’s)

a magnetic field is produced by an

electric current (ampere’s law)

maxwells equations - electric fields are produced by

• electric charges

• changing magnetic fields

maxwells equations - magnetic fields are produced by 

• electric currents 

• changing electric flux

in vacuum, away from all charges and currents, they become

• So if we can produce a changing magnetic field, we
  will get an electric field

•  If that electric field is also changing, we will get
  another magnetic field

• This process turns out to be coherent and leads to
  the existence of electromagnetic waves

electromagnetic waves are described in the

same way for other waves

but electromagnetic eaves are different from other waves in that they

do not require a medium

• they are not excitations of some material thing

• they are excitations of electric and magnetic fields 

the electric and magnetic fields oscillate in space in time:

• with the same wavelength, frequency, and pahse

• but with different amplitudes

the electric and magnetic fields are transverse waves, meaning that the electric and magnetic fields are 

always perpendicular to the direction the wave is traveling 

electromagnetic wave RHR1:

• Index Finger in direction of electric field

• Middle Finger in direction of magnetic field

• Thumb in direction of propagation

electromagnetic wave RHR2:

• point the fingers of the right hand in
  the direction of the electric field,

•  curl them toward the direction of the
  magnetic field

•  your thumb will point in the direction
  of propagation

as the wavelength decreases, 

frequency increases 

the speed of the wave is determined by

the medium through which it propagates

in vacuum, all electromagnetic waves travel at

the same speed, known as the speed of light

in matter, the speed depends on

the index of refraction of the medium, n

EM waves travel slower through

matter than they do through vacuum

the index of refraction for most materials depends on

wavelength/frequency

the wavelength of a wave depends on the

material through which it is propagating, as well

the frequency does not

change (assuming no energy loss) and it is independent of the material