- #1
zebediah49
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A positron and an electron are simultaneously fired from paralle particle accelerators a distance d apart, with equal velocity v.
One calculation says that each one will, being a moving charged particle, induce a magnetic field
[tex]
B=\frac{\mu_0 q v}{4\pi d^2}
[/tex]
and since the other is moving in that field, it experiences a force
[tex]
F=q v B = \frac{mu_0 q^2 v^2}{q\pi d^2}
[/tex]
As well as an effect from the electric field, but that's not a problem.
The other calculation says that if I transform to the coordinate frame of the moving particles, they are not moving, and thus there is no force due to magnetic interactions (just the electrostatic one).
I know that I can use a Lorentz transformation to convert the two fields without issue; I'm just not sure what happens with the interaction.
ALSO: could someone refresh me on the latex tag?
One calculation says that each one will, being a moving charged particle, induce a magnetic field
[tex]
B=\frac{\mu_0 q v}{4\pi d^2}
[/tex]
and since the other is moving in that field, it experiences a force
[tex]
F=q v B = \frac{mu_0 q^2 v^2}{q\pi d^2}
[/tex]
As well as an effect from the electric field, but that's not a problem.
The other calculation says that if I transform to the coordinate frame of the moving particles, they are not moving, and thus there is no force due to magnetic interactions (just the electrostatic one).
I know that I can use a Lorentz transformation to convert the two fields without issue; I'm just not sure what happens with the interaction.
ALSO: could someone refresh me on the latex tag?
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