Moving charges and magnetic fields

In summary: The particles on the charged plate do create a magnetic field that affects the particles in the wire.
  • #1
Jdo300
554
5
Hey,

I was just thinking about the simple concept that a moving electron produces a magnetic field at right angles to its travel... Now here's my question. Since we live in a relativistic universe, what is the charge moving with respect to in order to create the field? If we say the observer, then one is forced to conclude that the electron must always have a magnetic field around it since it is always going to be moving with respect to something... Where am I going wrong here?

- Jason O
 
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  • #2
Congratulations! You are thinking subtle and deep thoughts. The way to detect the presence of a magnetic field is to observe its force on a current, that is, on at least one moving test charge. Accordingly, you have a system of two (at a minimum) charges. If both move at the same speed as seen in the lab frame, then in their rest frames they see each other at rest and feel an electrostatic attraction or repulsion. In the lab frame they appear to be responding to each other's magnetic field.

The major, deep conclusion is that magnetism is just a relativistic manifestation of the Coulomb interaction. The precise relation is through the electromagnetic tensor, which you can look up in an advanced E&M book or online at, eg., Wikipedia.
 
  • #3
consider two cases, both with two electrons.

the first case is where the two electrons whiz by an observer with constant and identical velocities (both direction and speed, so they are not moving relative to each other). the observer concludes one electron is generating a magnetic field and the other electron is moving through the magnetic field and is therefore affected by it and the observer see that. there is, of course, the electrostatic interaction besides the magnetic interaction.

the other case is identical except now the observer is moving alongside the two moving electrons at their velocity. this is a constant velocity, an inertial frame of reference, so it is just as legitimate as any other inertial reference frame, including the one of the "stationary" observer in the first case above. but now what does the observer see? any magnetic field getting generated? from this observer's POV is the other electron moving through a magnetic field, even if one were generated? there remains the electrostatic interaction, though, in this reference frame even if there is no magnetic interaction.

both POVs are inertial and equally valid. how do you resolve the differences of observed behavior between the two?

you can do this thought experiment even better with two identical, infinite, and parallel lines of charge.
 
  • #4
Hello,

Thanks for the insights here. Ok, here's another question to, hopefully, clarify my understanding here. Let's say, for instance that there is a piece of wire with an AC current flowing through it, and next to this piece of wire we have a negatively charged plate. If we observe the electrons in the wire from the charged plate's prospective, one would expect to see a changing magnetic field exerting a force on the particles in the plate.

Now if one is in the wire moving with the flow of electrons in the wire, the particles on the plate would appear to be moving back and forth so this means that the charges on the plate would appear to be producing a magnetic field that is acting on the charges in the wire right?

- Jason O
 

1. What is the relationship between moving charges and magnetic fields?

The movement of electric charges creates a magnetic field around the charge. This magnetic field can then interact with other moving charges, causing them to experience a force. This relationship is described by the Lorentz force law, which states that the force on a charged particle is equal to the product of its charge, the velocity of the particle, and the strength of the magnetic field.

2. How do moving charges create a magnetic field?

When electric charges move, they create a magnetic field around them. This is due to the fact that moving charges have a magnetic dipole moment, which is a measure of the strength and orientation of their magnetic field. As the charges move, their magnetic fields interact and combine, creating a larger magnetic field around them.

3. Can magnetic fields affect the motion of charged particles?

Yes, magnetic fields can exert a force on charged particles, causing them to change their direction or velocity. This is known as the Lorentz force, and it is responsible for many phenomena, such as the deflection of charged particles in a magnetic field and the operation of electric motors and generators.

4. How are magnetic fields measured?

Magnetic fields are typically measured using a device called a magnetometer. This device uses a compass or a magnetically sensitive material to detect the strength and direction of the magnetic field. The unit for measuring magnetic fields is the tesla (T), with smaller units such as the gauss (G) also commonly used.

5. What are some applications of moving charges and magnetic fields?

Moving charges and magnetic fields have many important applications in modern technology. These include electric motors, generators, MRI machines, particle accelerators, and magnetic levitation trains. They also play a crucial role in understanding the behavior of celestial bodies, such as Earth's magnetic field and the interactions between the sun and other planets.

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