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Magnetic Fields and Relativity
Name: Muntaseer Al K.
Status: student
Age: 20s
Location: N/A
Country: N/A
Date: 10/25/2005
Question:
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 relative
phenomenon?
Replies:
Dear Al,
You undoubtedly have received excellent answers to this question already,
but I cannot help myself from putting in my two cents, though I am VERY late.
You show wisdom in saying magnetism is a "relative phenomenon". In fact
magnetism can be understood by combining electrostatics and relativity.
My favorite example (which I believe led Einstein to his theory of special
relativity) is to consider two protons (or any two objects in space each
carrying a positive charge) at rest relative to you. As you know, they will
repel each other with a force given by coulomb's law.
Now run past the charges. Since they are moving as seen by you, you will
see them each generate a magnetic field and feel an attractive force due to
moving through the magnetic field generated by the other charge. In fact,
if you could run at the speed of light (you cannot but you could get close,
in principle) the magnetic force would exactly cancel the electric force!
How could your running past the charges possibly change the force they exert
on each other? Nonetheless your running does! This can be explained by
relativity since if you see the charges moving past you (all motion is
relative so its the same whether you are running past the charges or they
are moving (in the opposite direction) past you), special relativity says
time in the system moving relative to you is dilated as measured by you.
Therefore the charges move apart more slowly. In fact, if the relative
speed is the speed of light, the time dilation is infinite and so you never
see the charges separate.
You could equally well explain this by saying the magnetic force just
cancels the electric force and so the charges never separate.
I hope this helps. It is a weird world!
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
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