Does a Magnetic Field Emerge from a Moving Charge with Constant Angular Speed?

In summary, the conversation discusses the emergence of a magnetic field when a charged particle moves with constant angular speed. The participants also mention the need to solve for potential fields and coordinates of the particle, as well as the presence of electric and magnetic fields in the far field. They suggest looking into classical electrodynamics textbooks for further information.
  • #1
Timothy S
49
0
If I write the lagrangian for a moving charge with constant angular speed, would a magnetic field be emergent? I would do the math myself, but I'm nowhere near pen and paper.
 
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  • #2
Timothy S said:
If I write the lagrangian for a moving charge with constant angular speed, would a magnetic field be emergent? I would do the math myself, but I'm nowhere near pen and paper.
First of all, if there is no magnetic field to begin with why would a charge spin in circles? Spinning in circles implies there is some kind of force, because there is a centripetal acceleration, without centripetal acceleration there is no circular motion.
 
  • #3
Alexandre said:
First of all, if there is no magnetic field to begin with why would a charge spin in circles? Spinning in circles implies there is some kind of force, because there is a centripetal acceleration, without centripetal acceleration there is no circular motion.

A charged pith ball on the edge of a rotating disk, driven at constant angular velocity, would suffice.
 
  • #4
stedwards said:
A charged pith ball on the edge of a rotating disk, driven at constant angular velocity, would suffice.
I think you need to solve for potential field and coordinate of the particle. But I'm not sure how, check this out
https://people.ifm.liu.se/irina/teaching/sem4.pdf
 
  • #5
Alexandre said:
I think you need to solve for potential field and coordinate of the particle. But I'm not sure how, check this out
https://people.ifm.liu.se/irina/teaching/sem4.pdf

For whatever reason, that solution seems to leave out the fields generated by the accelerating charge, though I only scanned the paper. There should be a magnetic field in the far field having an intensity something like ##B_z(r,\theta) = (1/r^2 sin \theta) cos(\omega t +f(\rho,t))##, in standard spherical coordinates, accompanied by a perpendicular electric field.
 
  • #6
I'm not sure, what the question is about. If you have given the motion of a charge, maybe you want to know the electromagnetic field due to this moving charge. You find this problem for circular motion in almost any textbook on classical electrodynamics. Look for synchrotron radiation. A good treatment can be found in Landau/Lifshitz vol. II and, of course, Jackson, Classical Electrodynamics.
 
  • #7
Sorry it was a really stupid question on so many levels.
 

Related to Does a Magnetic Field Emerge from a Moving Charge with Constant Angular Speed?

1. What is the Lagrangian of moving charge?

The Lagrangian of moving charge is an expression used in classical mechanics to describe the energy of a charged particle moving in an electromagnetic field. It is a function that takes into account the kinetic energy of the particle, the potential energy from the electric and magnetic fields, and any external forces acting on the particle.

2. How is the Lagrangian of moving charge calculated?

The Lagrangian of moving charge is calculated using the equation L = T - V, where T is the kinetic energy of the particle and V is the potential energy from the electric and magnetic fields. The kinetic energy is calculated using the particle's mass and velocity, while the potential energy is calculated using the particle's charge and the electric and magnetic field strengths.

3. What is the significance of the Lagrangian of moving charge?

The Lagrangian of moving charge is significant because it allows us to analyze the motion of charged particles in an electromagnetic field using the principles of classical mechanics. It also helps us understand the relationship between the electric and magnetic fields and their effects on the charged particle's motion.

4. Can the Lagrangian of moving charge be used to describe the motion of all charged particles?

Yes, the Lagrangian of moving charge can be used to describe the motion of all charged particles, regardless of their mass or charge. This is because the equation takes into account both the particle's kinetic and potential energy, making it applicable to all types of charged particles.

5. How does the Lagrangian of moving charge relate to other physical principles?

The Lagrangian of moving charge is related to other fundamental principles in physics, such as the principle of least action and Hamilton's equations of motion. It is also closely connected to Maxwell's equations, which describe the behavior of electromagnetic fields, and can be used to derive them from a more fundamental perspective.

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