Magnetic field of a moving charge

In summary, the magnetic field of a moving charge is described by the inverse square law, but from far away, it appears as a dipole moment with an inverse cube law. However, when using the formula for dipole moment, a moving charge with a localized current distribution appears to have a zero dipole moment. This is because the formula does not account for non-stationary current distributions.
  • #1
Ahmes
78
1
The magnetic field of a moving charge is:
[tex]\boldsymbol{B} = \frac{\mu_0}{4\pi} \frac{q \boldsymbol{v}\times \boldsymbol{\hat{r}}}{r^2}[/tex]
This is an inverse square law.

But also we know that every localized current distribution (and a moving particle is most obviously a localized current distribution) appears from very far away as a dipole moment - which field is an inverse cube law.

Also using [itex]\boldsymbol{m} = \iiint \boldsymbol{x} \times \boldsymbol{J}(\boldsymbol{x}) d^3 x[/itex] it appears a moving charge, [itex]\boldsymbol{J}=q \boldsymbol{v} \delta^3 (x)[/itex] has a zero dipole moment.

So how could this be explained?
Thank you.
 
Last edited:
Physics news on Phys.org
  • #2
A moving charge is a non stationary current distribution, so the last two formulae are no longer valid to describe its magnetic field.
 
  • #3
When Jackson develops these formulae he doesn't demand the current distribution to be stationary, although I can see why it is not.
OK, thank you.
 

What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges, such as electrons, and can exert a force on other moving charges.

How is a magnetic field created by a moving charge?

A magnetic field is created when a charged particle, such as an electron, moves through space. The movement of the charged particle creates a magnetic force that forms a circular pattern around the particle's path.

What is the relationship between a magnetic field and a moving charge?

A moving charge creates a magnetic field, and the strength of the magnetic field depends on the speed of the charge and the distance from the charge. The direction of the magnetic field is perpendicular to the direction of the charge's movement.

How does the direction of a magnetic field change with the direction of a moving charge?

The direction of a magnetic field changes as the direction of a moving charge changes. If the charge changes direction, the direction of the magnetic field also changes, always remaining perpendicular to the charge's motion.

What is the significance of a magnetic field in everyday life?

Magnetic fields play a crucial role in many everyday technologies, such as electric motors, generators, and MRI machines. They also help protect Earth from harmful solar radiation and are used in compasses for navigation.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
1K
  • Classical Physics
Replies
4
Views
687
  • Advanced Physics Homework Help
Replies
8
Views
5K
Replies
6
Views
1K
  • Advanced Physics Homework Help
Replies
9
Views
614
Replies
6
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
Replies
5
Views
2K
Replies
1
Views
271
  • Advanced Physics Homework Help
Replies
1
Views
2K
Back
Top