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amarcu
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 Posted: Fri Nov 21, 2008 12:20 am Post subject: Interactions between moving charged particles |
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Can anyone help me understand how moving charged particles interact?
Let>s start with two electrons moving parallel to each other, in the
same direction and same speed. Do they create magnetic fields? Is
there a magnetic attractive force between them (on top of the
repulsive electric force)? Please keep the math simple if any. Thanks |
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Tom Roberts
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| Posted: Fri Nov 21, 2008 10:05 pm Post subject: Re: Interactions between moving charged particles |
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amarcu wrote:
[quote]Can anyone help me understand how moving charged particles interact?
Let>s start with two electrons moving parallel to each other, in the
same direction and same speed. Do they create magnetic fields? Is
there a magnetic attractive force between them (on top of the
repulsive electric force)? Please keep the math simple if any. Thanks
[/quote]
Consider inertial frame S relative to which two free electrons are
moving, and at time t=0 in S they are moving parallel relative to S with
3-velocity v and are separated by a distance d.
In the instantaneously comoving inertial frame S' that moves with v
relative to S, the electrons are at rest at t=0, and so their electric
fields will cause them to move apart in this frame. In S that implies
that the distance between them increases with time, being larger than d
after t=0.
In S' at time' corresponding to t=0, the electrons are at rest relative
to each other and relative to S', so at this time' they each generate a
purely electric field. For other time>s they are moving relative to S'
and thus generate both electric and magnetic fields in S'.
In S, at t=0 the electrons are moving, so they generate both electric
and magnetic fields. Both must be applied to determine their motion. As
they move apart in S', they must move apart in S, so it is clear that
the effect of the electric field (repulsive) is greater than the effect
of the magnetic field (here attractive).
Tom Roberts |
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amarcu
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| Posted: Fri Nov 21, 2008 10:11 pm Post subject: Re: Interactions between moving charged particles |
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Hey Tom,
Thanks for the reply. You already took my little exercise to the next
level and actually played it backwards. I was planning to involve
relativity a bit later. Let>s just stick to one frame of reference for
now, in which the electrons are moving parallel with some velocity v
at a distance d. From what I know the repulsive electric force is
proportional to 1/d^2 and the magnetic field intensity B (so the
magnetic force too) is proportional to 1/d. I didn>t run the numbers
but it looks like there should be a distance of equilibrium d=f(v)
beyond which the attractive magnetic force surpasses the repulsive
electric force. If that>s not the case please explain why, keeping
relativity out of it for now. Thanks |
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amarcu
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| Posted: Sat Nov 22, 2008 4:30 am Post subject: Re: Interactions between moving charged particles |
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On a second thought I might be wrong about 1/d for the magnetic field.
It could be 1/d^2, same as for the electric field. I>m not sure at
this point. Can someone help with the magnetic field equation for a
moving free electron? Please keep it simple though: linear motion
along the x axes, constant velocity. |
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amarcu
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| Posted: Sat Nov 22, 2008 4:35 am Post subject: Re: Interactions between moving charged particles |
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On a second thought I might be wrong about 1/d for the magnetic field.
It could be 1/d^2, same as for the electric field. I>m not sure at
this point. Can someone help with the magnetic field equation for a
moving free electron? Please keep it simple though: linear motion
along the x axis, constant velocity. |
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amarcu
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| Posted: Sun Nov 23, 2008 2:26 pm Post subject: Re: Interactions between moving charged particles |
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Anyone?
I tried to find it on the net but all I get is related to the
interaction of a free electron with an external magnetic field, not
the field produced by the electron itself. |
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