Is the Theory of Magnetism and Relativity Flawed?

[nassboy]

I've seen in feynman and on the internet a derivation that the force on a negatively charged particle from neutral current carrying wire can be shown to be purely magnetostatic in one frame of reference and purely electrostatic in the other frame of reference using the length contraction. The contracted wire has a net positive charge, and therefore attracts the negatively charged particle.

I've tried to extend this idea to two current carrying wires(the direction of the current the same in both wires)...but it seems that they both would have positive charge and repel when they should attract.

What am I doing wrong?

 

[tiny-tim]

I've seen in feynman and on the internet a derivation that the force on a negatively charged particle from neutral current carrying wire can be shown to be purely magnetostatic in one frame of reference and purely electrostatic in the other frame of reference using the length contraction.

Hi nassboy!

That doesn't look right …

E² - B² is invariant (independent of the frame of reference), so you can't have the same field with just E or just B in different frames.

 

[nassboy]

This website describes what I'm talking about...

http://physics.weber.edu/schroeder/mrr/MRRtalk.html

 

[tiny-tim]

This website describes what I'm talking about...

http://physics.weber.edu/schroeder/mrr/MRRtalk.html

But where does the purely electrostatic / purely magnetostatic thing come from?

 

[Creator]

I've seen in feynman and on the internet a derivation that the force on a negatively charged particle from neutral current carrying wire can be shown to be purely magnetostatic in one frame of reference and purely electrostatic in the other frame of reference using the length contraction. The contracted wire has a net positive charge, and therefore attracts the negatively charged particle.

I've tried to extend this idea to two current carrying wires(the direction of the current the same in both wires)...but it seems that they both would have positive charge and repel when they should attract.

What am I doing wrong?

Nassboy...
You are failing to take into account the Magnetic fields, in particular the DIRECTION of each B field around each wire.This is the same mistake 'meemoe_uk' was making in a previous thread, (except he would never admit it).

Remember the purpose of that exercise is to derive the MAGNETIC FIELD around the wire...

The DIRECTION of that field around each wire DETERMINES the direction of the force (in the lab frame) on a test charge or upon ANOTHER CURRENT A CARRYING WIRE according to the Lorentz force equation (below)...

F = qv X B (for point charges) (B = mag.field; q = test charge with velocity v outside the wire)

F = Integral ( IL X B) ...( for wires) (where L = length of wire, I = current)
(Your link doesn't point that out very well).
Remember these are the forces YOU as the observer sees in the lab frame.

(Actually, the full Lorentz equaton is F = qE + (qv X B)...but the electric field E is zero in the lab frame since the each wire is electrically neutral in labe frame).

And remember its the 'right hand rule' that determine the direction of the force.
See here for a little more: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html

Creator

P.S. the link you cited is not a very great explanation since it arrived at the "magnetic force" (eqn. # 3) in somewhat non traditional form...and without the Lorentz force eqn. you cannot see in which direction that force is acting.

However, you will see that the mag. force eqn. (equation # 3 in your link) is the same as my equation above because the term in the parenthesis is simply equal to B...IOW, simply substitute B = uI / 2(pi)R (Ampere's law) for the term in parenthesis and you will recover Lorentz force equation I gave above.)

see:http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/magcur.html

 

[marcusl]

I've seen in feynman and on the internet a derivation that the force on a negatively charged particle from neutral current carrying wire can be shown to be purely magnetostatic in one frame of reference and purely electrostatic in the other frame of reference using the length contraction. The contracted wire has a net positive charge, and therefore attracts the negatively charged particle.

I've tried to extend this idea to two current carrying wires(the direction of the current the same in both wires)...but it seems that they both would have positive charge and repel when they should attract.

What am I doing wrong?

Let's put the same current in each wire so the mean electron drift velocities are equal. Each moving electron in wire 2 sees a net positive charge in wire 1--this is the case that you say Feynman considers--so the electrons are attracted towards the other wire. The positive copper ions in wire 2 are at rest, however. They see an electrically neutral wire 1, and feel no force. The system is symmetric, so everything we said about wire 2 applies also to wire 1. The mutual force is attractive.

Creator: you've missed the point of this thread. The OP's link demonstrates the relativistic unity of electric and magnetic forces.

 

[nassboy]

I still don't see why both wires aren't length contracted and therefore have a positive charge...

Only one wire is moving and not both?

 

[jostpuur]

I've seen in feynman and on the internet a derivation that the force on a negatively charged particle from neutral current carrying wire can be shown to be purely magnetostatic in one frame of reference and purely electrostatic in the other frame of reference using the length contraction.

Hi nassboy!

That doesn't look right …

E² - B² is invariant (independent of the frame of reference), so you can't have the same field with just E or just B in different frames.

It is possible that $\boldsymbol{E}=0$ and $\boldsymbol{B}\neq 0$ in some frame, so that a particle feels only a magnetic force, and $\boldsymbol{E}\neq 0$ and $\boldsymbol{B}\neq 0$ and $\boldsymbol{v}=0$ in some other frame, so that a particle feels only an electric force.

 

[marcusl]

I still don't see why both wires aren't length contracted and therefore have a positive charge...

Only one wire is moving and not both?

The wires aren't moving, only the electrons in the wires.

 

[lovetruth]

I've seen in feynman and on the internet a derivation that the force on a negatively charged particle from neutral current carrying wire can be shown to be purely magnetostatic in one frame of reference and purely electrostatic in the other frame of reference using the length contraction. The contracted wire has a net positive charge, and therefore attracts the negatively charged particle.

I've tried to extend this idea to two current carrying wires(the direction of the current the same in both wires)...but it seems that they both would have positive charge and repel when they should attract.

What am I doing wrong?

If they both have positive charge they should have repulsive electrostatic force. But the attractive magnetic force due to moving proton will be more. Thus the total force on wire will be attractive. U failed to see the magnetic force.

 

[Doc Al]

There is nothing wrong with your understanding. The problem is in the relativity theory and the eroneous derivation by feynmann. I kno i am challenging Feynman and einstein authority but, please read my explanation below for what is wrong in both the theory and derivation. I will only consider the charges(proton and electron) in the wire.

So far so good for the magnetostatic case. The real error is done in electrostatic case.

For the electrostatic case,
the proton are at rest so their length is more in this frame than in the magnetostatic frame. The proton density is reduced in the electrostatic case. This increase in length of proton in electrostatic case is ignored in the derivation. The protons length was contracted when the protons were moving in the magnetostatic case. If the protons come at rest in electrostatic frame, they must come to their orignal length which is greater than in magnetostatic frame(in which proton length contraction occur).
electron length will contract and increase electron density(which is correctly shown in the derivation), but proton length expansion is ignored in derivation.
Now u kno the error in derivation.
Even after accounting the error done in derivation, relativity theory gives different result. thus, the theory must be wrong.

Nonsense. Length contraction is most definitely considered.