Moving Magnet and Conductor Problem - Transformation of Fields As Predicted By Maxwell's Equations

Transformation of Fields As Predicted By Maxwell's Equations

See also: Classical electromagnetism and special relativity

In 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.

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