OK - it's not a homework problem... But, if you've ever wondered about the nature of light and how it relates to space-time here's a little something to dream about.
The velocity of EM propagation in free space (the velocity of light, 'c') is determined from Maxwell's Eqs. by:
c = 1/sqrt(epsilon0 * mu0)
epsilon0 is the permittivity of free (empty) space and mu0 is the permeability of free space. They are usually just viewed as calibration or scale factors (constants of proportionality) chosen so that various quantities and units of measurement work out in convenient terms. They are thus regarded as having no physical significance since empty space is viewed as having no actual dynamic physical properties. epsilon0 and mu0 are therefore the base standard for evaluating electric and magnetic field interaction (with themselves and their surroundings) since empty space is regarded as possessing the absolute minimum ability to interact with (i.e. to either enhance or diminish) either phenomena.
Permittivity and permeability are basically quantities that relate to the responsiveness of a medium to accomodate or manifest an electric (for permittivity) or magnetic (for permeability) field. They are both expressed as ratios between a force field density to that of a given applied field strength. Permittivity is the ratio of charge density for a given applied electric field strength. Permeability is the ratio of magnetic flux density ("lines of force" per square spatial unit) to that of a given magnetic field strength.
The strange thing is that these quantities do have physical significance as they relate to any medium other than a vacuum. They are both related to the nature of how a substance manifests their particular energy forms and how the manifestation is propagated through the material. A little study regarding permittivity and permeability reveals that both bear a striking resemblence to how strain propagates through an elastic medium. Coincidence? I don't think so.
See: http://www.geocities.com/ResearchTriangle/Forum/9850/ect.pdf
for an interesting paper on how permittivity and permeability imply a relationship to spacetime elasticity.
Perion
The velocity of EM propagation in free space (the velocity of light, 'c') is determined from Maxwell's Eqs. by:
c = 1/sqrt(epsilon0 * mu0)
epsilon0 is the permittivity of free (empty) space and mu0 is the permeability of free space. They are usually just viewed as calibration or scale factors (constants of proportionality) chosen so that various quantities and units of measurement work out in convenient terms. They are thus regarded as having no physical significance since empty space is viewed as having no actual dynamic physical properties. epsilon0 and mu0 are therefore the base standard for evaluating electric and magnetic field interaction (with themselves and their surroundings) since empty space is regarded as possessing the absolute minimum ability to interact with (i.e. to either enhance or diminish) either phenomena.
Permittivity and permeability are basically quantities that relate to the responsiveness of a medium to accomodate or manifest an electric (for permittivity) or magnetic (for permeability) field. They are both expressed as ratios between a force field density to that of a given applied field strength. Permittivity is the ratio of charge density for a given applied electric field strength. Permeability is the ratio of magnetic flux density ("lines of force" per square spatial unit) to that of a given magnetic field strength.
The strange thing is that these quantities do have physical significance as they relate to any medium other than a vacuum. They are both related to the nature of how a substance manifests their particular energy forms and how the manifestation is propagated through the material. A little study regarding permittivity and permeability reveals that both bear a striking resemblence to how strain propagates through an elastic medium. Coincidence? I don't think so.
See: http://www.geocities.com/ResearchTriangle/Forum/9850/ect.pdf
for an interesting paper on how permittivity and permeability imply a relationship to spacetime elasticity.
Perion
