ELECTROMAGNETISM

CURRENTS AND MAGNETIC FIELDS:

• Current:
  electric current = ordered flow of electric charge,
  = rate at which charge moves past a reference point:

  

  unit of current = 1 Ampère = 1A = 1 Coulomb/second

• charges generate electric fields -- currents generate magnetic fields
• other way of stating same thing:
  all charges generate electric fields --
  moving charges also generate magnetic fields
• a straight current carrying wire generates a cylindrical magnetic field in the space surrounding it
  (magnetic field lines are circles around the wire)

• magnetic force on moving charge - ``Lorentz force'':
  magnetic fields exert force on moving charges,

  

  (B is the magnetic field strength, v the velocity of the charge q)
  force is perpendicular to both magnetic field and velocity
  no force when motion parallel to magnetic field

• electric fields act on all charges --
  magnetic fields act only on moving charges
• unit of magnetic field = 1 Tesla = 1 T
  1 Tesla = 1 Newton / (Ampère meter)

ELECTROMAGNETIC INDUCTION

• flux of the field:
  flux of the field through a surface = the total net number of fieldlines penetrating the surface.
  For a uniform field B,
  the flux is just the product of the field strength and the ``effective'' area of the surface; the effective area is the area ``offered'' to or ``penetrated'' by the fieldlines (i.e. the equivalent area perpendicular to the field). All other things equal, the flux is maximal if the surface is perpendicular to the field direction; it is = zero if the surface is parallel to the field direction.
• Faraday's law of induction
  When the magnetic flux through the surface enclosed by a wire loop changes, an ``electromotoric force'' (voltage) is ``induced'' in the wire loop.
  The induced voltage is equal to the rate of change of the flux:

  

• ways to change the flux:
  • - vary the field strength
  • - move the wire loop in and out of the field area (or move the wire loop in a non-uniform field)
  • - change the area enclosed by the wire loop (e.g. by deforming it)
  • - change the angle between the wire loop and the field direction (e.g. by rotating the wire loop)
• induction is the basis of the ``generators of electricity'' that run in electric power plants.

ELECTROMAGNETIC RADIATION

• MAXWELL'S EQUATIONS: are four differential equations summarizing nature of electricity and magnetism: (formulated by James Clerk Maxwell around 1860):

  

  

  

  • (1) Electric charges generate electric fields.

  • (2) Magnetic field lines are closed loops; there are no magnetic monopoles.

  • (3) Currents and changing electric fields produce magnetic fields.

  • (4) Changing magnetic fields produce electric fields.

  Together with the equation for the Lorentz force, these equations describe all electromagnetic phenomena (i.e. all electromagnetic phenomena can be derived from them.)
  

• from Maxwell's equations one can derive another equation which has the form of a ``wave equation''.
  This differential equation was known from mechanics to have solutions which describe wave phenomena in mechanics.
  From this, Maxwell concluded that there should be also solutions to the wave equation derived from his equations
  -- ``electromagnetic waves'', corresponding to the propagation of oscillations of the electric and magnetic fields.

• speed of electromagnetic waves
  is also derived from this wave equation, expressed in terms of constants which appear in the relation between charge and electric field (k in Coulomb's law) and between current and magnetic field ( in Ampère's law).
  This speed turns out to be = the speed of light!
• Conclusion and prediction:
  - light is just a form of electromagnetic radiation
  - there should be other forms of electromagnetic radiation (different frequencies) which can be produced by making charges ``wiggle''
• This was experimentally verified by Heinrich Hertz:
  (built device to generate e.m. waves - first human-made radio waves)

ELECTROMAGNETIC WAVES:

• electromagnetic radiation = coupled, oscillating electric and magnetic fields moving through space at the speed of light;
  magnetic and electric fields ``feed on each other'',
  obeying Maxwell's 3rd and 4th laws
• e.m. waves do not need material carrier - move through vacuum
  (- no ``ether'')
• e.m. waves are transverse waves - electric field perpendicular to magnetic field, both perpendicular to direction of propagation
• speed of light = 300 000 km/sec = 186 000 miles/second
  (this is the speed of light in vacuum) (speed of light in air is very similar)
• electromagnetic waves generated by accelerating charges

TYPES OF ELECTROMAGNETIC WAVES:
(distinguished by different frequency and wavelength range)

• radio waves
• microwaves
• infrared
• visible light
• ultraviolet
• X-rays
• rays

INTERACTION OF E.M. WAVES WITH MATTER
when hitting matter, e.m. wave can undergo transmission, absorption, or scattering (in general, some of all of these)

• transmission
  wave passes through matter, usually at different speed (depending on ``refractive index'' of material)
  change in direction of wave due to different speed = ``refraction''
• absorption
  energy carried by wave ``absorbed'' (soaked up) by material, usually converted into heat.
• scattering
  = absorption with subsequent re-emission
  can be diffuse scattering or reflection

ELECTROMAGNETIC SPECTRUM

Historical Note:

• James Clerk Maxwell (1831-1879), (Prof.Physics in Aberdeen, London, Cambridge)
  - theory of heat,
  - kinetic gas theory (Maxwell-Boltzmann velocity distribution),
  - theory of electricity and magnetism
• Heinrich Hertz (1857-1894) (Prof. Physics Karlsruhe, Bonn)
  - experimental observation of electromagnetic radiation (1887)
  (radio waves)
  - influence of UV light on electric discharges