Magnetic Fields and Relativity
Suppose a spaceship is moving with a constant velocity
with respect to an observer. Also imagine that an electron in the
spaceship is at rest with respect to the spaceship. therefore an
observer in spaceship suppose to detect no magnetic field around the electron
since it is at rest with respect to him and according to postulate of
special relativity laws of science are same in all inertial frame. But
an observer who notices both the spaceship and the electron are moving
with the same velocity with respect to him must detect a magnetic field
perpendicular to the motion of the electron since moving charge
creates magnetic field.
What should be the answer of this paradox? Is magnetic field is a
To detect the magnetic field, the electron must be moving relative to
the instrument that the observer is using to detect it. Let us assume
the detector is a coil of wire. On the spaceship, the electron,
observer, and detector are moving at the same velocity, the electron
never passes through the detector and no magnetic field is observed.
For the stationary observer, as the spaceship and electron pass through
his detector (a very big one!) he will see the magnetic field.
The observer at rest to the electron sees only an electric field.
However when one moves over to a moving frame of reference, some of this
electric field gets transferred into magnetic field. There is a math
relation between the electric and magnetic field. This is generally
discussed in many books on electromagnetic field theory, the sloshing of
energy from one to another, by Lorentz transformation.
Perhaps another way to look is to see that the (electric) field line
from a stationary charge just go out radially, out from the center. But
as the charge begins to move, the field lines going out, but into the
direction of travel seem to get dragged back. This gives rise to an
magnetic field in this (moving)frame. Electric and Magnetic are two
sides of the same thing in special relativity.
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Update: June 2012