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Electromagnetic waves. Hecht, Chapter 2 Monday October 21, 2002. Electromagnetic waves. Consider propagation in a homogeneous medium (no absorption) characterized by a dielectric constant .  o = permittivity of free space. Electromagnetic waves.

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electromagnetic waves

Electromagnetic waves

Hecht, Chapter 2

Monday October 21, 2002

electromagnetic waves1
Electromagnetic waves
  • Consider propagation in a homogeneous medium (no absorption) characterized by a dielectric constant

o = permittivity of free space

electromagnetic waves2
Electromagnetic waves

Maxwell’s equations are, in a region of no free charges,

Gauss’ law – electric field

from a charge distribution

No magnetic monopoles

Electromagnetic induction

(time varying magnetic field

producing an electric field)

Magnetic fields being induced

By currents and a time-varying

electric fields

µo = permeability of free space (medium is diamagnetic)

electromagnetic waves3
Electromagnetic waves

For the electric field E,

or,

i.e. wave equation with v2 = 1/µo

electromagnetic waves4
Electromagnetic waves

Similarly for the magnetic field

i.e. wave equation with v2 = 1/µo

In free space,  =  o = o ( = 1)

c = 3.0 X 108 m/s

electromagnetic waves5
Electromagnetic waves

In a dielectric medium,  = n2 and =  o = n2 o

electromagnetic waves phase relations
Electromagnetic waves: Phase relations

The solutions to the wave equations,

can be plane waves,

electromagnetic waves phase relations1
Using plane wave solutions one finds that,

Consequently

Electromagnetic waves: Phase relations

i.e. B is perpendicular to the

Plane formed by k and E !!

electromagnetic waves phase relations2
Electromagnetic waves: Phase relations
  • Since also
  • k  E and k  B ( transverse wave)
  • Thus, k, E and B are mutually perpendicular vectors
  • Moreover,
electromagnetic waves phase relations3
Electromagnetic waves: Phase relations

Thus E and B are in phase since,

requires that

E

k

B

irradiance energy per unit volume
Irradiance (energy per unit volume)
  • Energy density stored in an electric field
  • Energy density stored in a magnetic field
energy density
Energy density

Now if E = Eosin(ωt+φ) and ω is very large

We will see only a time average of E

intensity or irradiance
Intensity or Irradiance

In free space, wave propagates with speed c

c Δt

A

In time Δt, all energy in this volume passes through A.

Thus, the total energy passing through A is,

intensity or irradiance1
Intensity or Irradiance

Power passing through A is,

Define: Intensity or Irradiance as the power per unit area

intensity in a dielectric medium
Intensity in a dielectric medium

In a dielectric medium,

Consequently, the irradiance or intensity is,

poynting vector1
Poynting vector

For an isotropic media energy flows in the direction of propagation, so

both the magnitude and direction of this flow is given by,

The corresponding intensity or irradiance is then,

example lasers
Example: Lasers

o = 8.854 X 10-12 CV-1m-1 (SI units)

Laser Power = 5mW

Same as sunlight at earth

Near breakdown

voltage in water

nb. Colossal dielectric constant material CaCu3Ti4O12 , = 10,000 at 300K

Subramanian et al. J. Solid State Chem. 151, 323 (2000)