# magnetic field strength paradox-where is my error in reasoning?

Under the assumption that I understood the following circumstances correct:

Magnetism occurs when a charged particle moves with a certain velocity through space. Faster velocity equals a stronger magnetic field,if the charge of the particle stays the same. Particle with the velocity zero (0) produce no measurably magnetic field.

I have the following question:

If our earth moves with the track speed of $29,78\,\mathrm{km/s}$ around the sun. And our sun moves with $3,05\,\mathrm{km/s}$ around the middle of the Milky Way. And the Milky Way moves with $x\,\mathrm{km/s}$ around the balance point of our local galaxy cluster. . . .

And I add all those velocities together,referring to a space fixed reference system far outside of our local cluster.Then it is highly unlikely that the velocity of the earth (in this reference system) is zero.

Then there should exist no charged particle with a magnetic field strength of zero(0) at all on our entire planet.Because our planet moves with a certain velocity,and therefore all charged particles,even if they rest in the reference system of the planet(0 km/s) move with the same velocity as the planet does.

Why is it possible on our planet,that charged particles can have a magnetic field strength of zero at all ?

The answer is probably very easy,but i cant wrap by head around it ,sorry ;)

• It's relative velocity in the observer's frame that matters. There is no absolute frame. – Rob Jeffries Oct 12 '15 at 18:55
• Particle with the velocity zero (0) produce no measurably magnetic field. The velocity term in the Lorentz force equation refers to the velocity of a charged particle relative to the source of the magnetic field. – HDE 226868 Oct 12 '15 at 18:56
• @HDE226868 No, the velocity in the Lorentz Force Law is the velocity relative to the frame that has a particular magnetic field. – Timaeus Oct 12 '15 at 19:53
• @Timaeus Semantics. :-) The point is, the source of the magnetic field can be at rest relative to anything else and still generate a magnetic field, because there's no absolute reference frame for it to be at rest in, meaning that if the velocity in the equation somehow referred to the velocity of the source, then there would be a paradox. – HDE 226868 Oct 12 '15 at 19:55

Magnetism occurs when a charged particle moves with a certain velocity through space.

No, current and time rates of change of current both contribute to magnetic fields. And so velocity of charges and their acceleration both contribute. In fact, at larger distances the magnetic field from the acceleration can be stronger.

Faster velocity equals a stronger magnetic field,if the charge of the particle stays the same. Particle with the velocity zero (0) produce no measurably magnetic field.

If our earth moves with the track speed of $29,78\,\mathrm{km/s}$ around the sun. And our sun moves with $3,05\,\mathrm{km/s}$ around the middle of the Milky Way. And the Milky Way moves with $x\,\mathrm{km/s}$ around the balance point of our local galaxy cluster. . . .

In a sense. Keep in mind that both positive and negative charges and both going in these directions.

And I add all those velocities together, referring to a space fixed reference system far outside of our local cluster.Then it is highly unlikely that the velocity of the earth (in this reference system) is zero.

There isn't really a frame that is that large, the word general in general relativity comes from not forcing the inertial frames to be global and only requiring that they be local and hold in a small region for a small time.

And also no frame is better than another. So if the frame the velocity were not were zero there would be another different frame moving with respect to the first where is was.

And here's the kicker. If you see just an electric field (and a zero magnetic field), a different frame can see a magnetic field and an electric field. Electric and magnetic fields are like velocity itself, people in different frames can disagree about them.

Then there should exist no charged particle with a magnetic field strength of zero(0) at all on our entire planet.

Experimentally its the opposite. Charged particles have an intrinsic magnetic moment proportional to their spin. So even when at rest there is a small dipole magnetic field.

Because our planet moves with a certain velocity,and therefore all charged particles,even if they rest in the reference system of the planet(0 km/s) move with the same velocity as the planet does.

In the local frame of the planet there is no motion, hence you don't need a motion induced magnetic field.

Why is it possible on our planet,that charged particles can have a magnetic field strength of zero at all ?

Again. Experimentally that's wrong. So I don't know why you'd say that. We don't have to theoretically explain a fact that experimentally doesn't happen.

As long as the electric field is stronger than the magnetic field, there is a frame in which there is no magnetic field. The strong magnetic fields we get, we get from having electric fields from many charges that cancel in a way where the magnetic fields from the charges reinforce each other. Such as a ring of positive charge at rest with an equal number of negative charges going clockwise in a circle on top.