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## Main Question or Discussion Point

Hi all,

I have been struggling mightily through Purcell's book on Electricity and Magnetism, but chapter 5, which deals with the SR explanation of magnetism has me somewhat confused.

Suppose we take the following scenario:

In the Lab frame, F, electron 2 (e2) is moving towards the right with velocity v, while electron 1 (e1) is stationary. In Purcell's section "Force on a moving charge", he shows that

Force

where Force

Anyway, in the following example in the same page, he assumes both e1 and e2 are at rest in the Lab frame, and then calculates

Force

To me, this makes sense also, because in the moving frame, e2 would then appear to be moving, and so its E field is increased by γ. However, Purcell argues that this cannot be true since

1) So my first question is what have I understood wrongly?

In his next section he talks about interaction between a moving charge and other moving charges. In his setup, e2 is replaced by a current carrying wire. He first explains the assuming the electrons are moving to the right with speed v, and the protons are fixed, the linear density of electrons will be equal to that of the protons, and therefore e1 will experience no electric force.

2) My second question is how can that be true? Shouldn't the density of the electrons be increased by γ thereby introducing an E field perpendicular to v?

I appreciate any help here.

thanks,

Aaron

I have been struggling mightily through Purcell's book on Electricity and Magnetism, but chapter 5, which deals with the SR explanation of magnetism has me somewhat confused.

Suppose we take the following scenario:

In the Lab frame, F, electron 2 (e2) is moving towards the right with velocity v, while electron 1 (e1) is stationary. In Purcell's section "Force on a moving charge", he shows that

Force

_{12}= γ.Force_{12}'where Force

_{12}is the force on e1 due to e2. This makes sense to me since the electric field due to e2 will be larger in the Lab frame because e2 is moving. He then goes on to state a simple rule that, "*The transverse component of the force on a particle is larger in the frame of the particle than in any other frame*". This statement obviously applies in the when the source of the E field is moving relative to the particle.Anyway, in the following example in the same page, he assumes both e1 and e2 are at rest in the Lab frame, and then calculates

Force

_{12}' = γ.Force_{12}To me, this makes sense also, because in the moving frame, e2 would then appear to be moving, and so its E field is increased by γ. However, Purcell argues that this cannot be true since

*the force on a particle is larger in the frame of the particle than in any other frame.*I don't understand the basis for this arguement. I thought the statement was just a general rule of thumb which he introduced assuming the particle was moving relative to the source of the E field acting on it.1) So my first question is what have I understood wrongly?

In his next section he talks about interaction between a moving charge and other moving charges. In his setup, e2 is replaced by a current carrying wire. He first explains the assuming the electrons are moving to the right with speed v, and the protons are fixed, the linear density of electrons will be equal to that of the protons, and therefore e1 will experience no electric force.

2) My second question is how can that be true? Shouldn't the density of the electrons be increased by γ thereby introducing an E field perpendicular to v?

I appreciate any help here.

thanks,

Aaron