# Suppose we have a proton and electron, separated with a distance d

## Main Question or Discussion Point

Suppose we have a proton and electron, separated with a distance, d with respect to a stationary observer. Another observer moves with velocity, v with respect to the proton & electron system, and measured that the distance between the proton and electron is D.
D < d by length contraction.
How could this be? The force between the two charged particles is an EM force dependent radially on the distance. Furthermore, if D < d, then does this mean that a moving atom shrinks in size?

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There will be magnetic fields as well since with respect to the second observer, the particles are moving.

There will be magnetic fields as well since with respect to the second observer, the particles are moving.
This magnetic field is a measured field between a particle and the observer, and not between the proton and electron, because both of them are stationary with respect to each other.
Further, if there really is magnetic field between electron and proton, as seen by a moving observer, then these would be magnetic monopoles.

jtbell
Mentor
The force between the two charged particles is an EM force dependent radially on the distance.
The electric field produced by a moving charge is not spherically symmetric. The component along the direction of motion is reduced so you get a sort of pancake-shaped distribution.

Magnetic monopoles? How did you get that?

The electric field produced by a moving charge is not spherically symmetric. The component along the direction of motion is reduced so you get a sort of pancake-shaped distribution.
Magnetic monopoles? How did you get that?
Perhaps my question was badly phrased or I don't get what you mean.
What I'm concern is the relative distance between a proton and an electron. Suppose I have a moving observer, say with speed v. Then, both proton and electron as seen by the observer is also moving with speed v. With Newtonian physics, the relative distance between the p and e stays the same as both moving with same speed.
With SR, the relative distance will contract, i.e. smaller than the proper distance. I view the distance as something like a ruler in the traditional textbook illustration.

If the distance is smaller (length contraction), then, with EM, this means the EM force is stronger. The component of the EM force being reduced along the direction of motion does not explain, nor does the non-spherical symmetric EM field of both particles,
because both of them are reduced by the same amount,
and what is of concern is the EM interaction between p and e but not with observer,
and a reduced EM component along the direction connecting p and e does not correspond to a shorter distance (length contraction) for EM attraction.

I was assuming quantum123 said that magnetic field exist between p and e. If that's so, that means both p and e now act like monopoles. But I agree that there would be magnetic fields, if there exist relative motion, but as measured by observer, not p or e. Sorry bout the confusion.

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Electric and magnetic monopoles are very different things.
In classical physics, there are no such thing as magnetic monopoles as they violate the Maxwell's equations.

Hurkyl
Staff Emeritus
Gold Member
The point is that if the proton is moving away from the electron, but exerts a magnetic force on the electron, that would be proof that the proton is a magnetic monopole. (And if the electron was moving towards the proton, that the electron is also a magnetic monopole)

In reality, the magnetic field caused by the proton is zero at the electron: think {velocity of proton} cross {displacement from proton to electron}.

(Actually, that would be the retarded velocity of the proton, and the displacement from the retarded position of the proton, but the distinction is irrelevant here)

So you define a monopole to be fields due to one particle, dipole the fields due to two particles, and N-pole to be the fields due to N particles?
That is wrong. In an oscillating antenna with 10^23 electrons, it is still called electric dipole! A rotating electron will give a magnetic dipole even if there is only one particle.
You have to look at the field lines to know what kind of N-pole you are talking about.

Hurkyl
Staff Emeritus