Transformation of Fields As Predicted By Maxwell's Equations
See also: Classical electromagnetism and special relativityIn a frame moving at velocity v, the E-field in the moving frame when there is no E-field in the stationary magnet frame Maxwell's equations transform as:
where
is called the Lorentz factor and c0 is the speed of light in free space. This result is a consequence of requiring that observers in all inertial frames arrive at the same form for Maxwell's equations. In particular, all observers must see the same speed of light c0. That requirement leads to the Lorentz transformation for space and time. Assuming a Lorentz transformation, invariance of Maxwell's equations then leads to the above transformation of the fields for this example.
Consequently, the force on the charge is
This expression differs from the expression obtained from the nonrelativistic Newton's law of motion by a factor of . Special relativity modifies space and time in a manner such that the forces and fields transform consistently.
Read more about this topic: Moving Magnet And Conductor Problem
Famous quotes containing the words transformation of, fields, predicted and/or maxwell:
“If you say, “I’m for equal pay,” that’s a reform. But if you say. “I’m a feminist,” that’s ... a transformation of society.”
—Gloria Steinem (b. 1934)
“For wheresoe’er I turn my ravished eyes,
Gay gilded scenes and shining prospects rise,
Poetic fields encompass me around,
And still I seem to tread on classic ground.”
—Joseph Addison (1672–1719)
“Is it not the chief disgrace in the world, not to be an unit;Mnot to be reckoned one character;Mnot to yield that peculiar fruit which each man was created to bear, but to be reckoned in the gross, in the hundred, or the thousand, of the party, the section, to which we belong; and our opinion predicted geographically, as the north, or the south?”
—Ralph Waldo Emerson (1803–1882)
“Hey, Steve, can a woman go nuts from gettin’ sawed in half too many times?”
—Griffin Jay, Maxwell Shane (1905–1983)