# Pair of moving charged particles

1. Feb 7, 2012

### zebediah49

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
$$B=\frac{\mu_0 q v}{4\pi d^2}$$
and since the other is moving in that field, it experiences a force
$$F=q v B = \frac{mu_0 q^2 v^2}{q\pi d^2}$$
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?

Last edited: Feb 7, 2012
2. Feb 7, 2012

### clem

Put tex in sqaure brackets before and /tex in sq. brackets after.
Use quote to see the latex file below:
$$B=\frac{\mu_0 q v}{4\pi d^2}$$

3. Feb 7, 2012

### clem

$${\bf F}=\frac{d{\bf p'}}{dt} =\frac{qq'[{\bf r}+{\bf v'\times(v\times r)}]} {\gamma_v^2[{\bf r}^2-({\bf v\times r)^2}]^{\frac{3}{2}}}.$$