Charges in Motion

FISMA

Lads,
Would love to hear your two cents on this. Am I missing something? Did I forget something?

As we know,
(1) a stationary charge has a constant electric field around it.
(2) a charge in motion with a constant velocity has a constant magnetic field around it.
(3) an accelerating charge has a changing magentic field - i.e. gives off "light."

However, all motion is relative. That charge that is stationary with respect to me, is most definitely in motion with respect to another observer.

So with respect to myself (no relative motion) the stationary charge has only an electric field, but no magnetic. However, with respect to another observer, (with whom there is relative motion), that same charge, has a magnetic field.

So, if this is true, the charge simultaneously does and does not have a magnetic field? Seems counter intuitive.

The main problem I am having is with the whole relative motion idea when it comes to E&M.

One of the most elegant feature of Maxwell's equations is that, since they are electromagnetic waves that go the speed of light, they need no relativistic correction. Even Einstein gave homage to Maxwell for this.

Please advise.

ZorbaTehZ

As you say, the Maxwell equations are Lorentz-invariant, so no adjustments need to be made (although technically they need to be put in a special vector form to make them look right.) Some very curious things appear to happen though when you look at the special relativistic E&M theory, for example in one frame what is purely a magnetostatical situation can appear as an electrostatical situation in another frame. It's a little convoluted to explain here, but length contraction comes in to play in "fixing" situations like you describe above if you consider specifically something like an B field being caused by a long conductor. I won't comment any further as I only started looking at the theory recently, for fear of saying something wrong.

FISMA

ZorbaTehZ wrote: »

... It's a little convoluted to explain here, but length contraction comes in to play in "fixing" situations like you describe above if you consider specifically something like an B field being caused by a long conductor. I won't comment any further as I only started looking at the theory recently, for fear of saying something wrong.

ZorbaTehZ - thanks and don't worry - comment away - if you're wrong, someone will correct you.

I don't mind being told when I am wrong. IMHO, the sooner I make the correction, the better.

Anyhow, in what class is this stuff taught? I never did any of this as an undergrad. What math do you need? Vectors and Tensors Calc?

Slan

ZorbaTehZ

FISMA wrote: »

Anyhow, in what class is this stuff taught? I never did any of this as an undergrad. What math do you need? Vectors and Tensors Calc?

A number of them, your standard electromagnetism class might do some, or you would do the complete in a class on the classical fields.

To understand it qualitatively then you don't need much, so long as you know the basic results from special relativity, and have some knowledge of electromagnetism, then that is more than sufficient. If you wish to do it properly, then you should know electromagnetism in the differential calculus formulation (which isn't too complicated, just tedious.)

Morbert

FISMA wrote: »

Lads,
Would love to hear your two cents on this. Am I missing something? Did I forget something?

As we know,
(1) a stationary charge has a constant electric field around it.
(2) a charge in motion with a constant velocity has a constant magnetic field around it.
(3) an accelerating charge has a changing magentic field - i.e. gives off "light."

However, all motion is relative. That charge that is stationary with respect to me, is most definitely in motion with respect to another observer.

So with respect to myself (no relative motion) the stationary charge has only an electric field, but no magnetic. However, with respect to another observer, (with whom there is relative motion), that same charge, has a magnetic field.

So, if this is true, the charge simultaneously does and does not have a magnetic field? Seems counter intuitive.

The main problem I am having is with the whole relative motion idea when it comes to E&M.

If we are facing a rubik's cube from different angles, we will see different colours, as each colour is on a face of the complete cube. And if the cube is rotated, or if we rotate out positions, we will see a different combination of colours again. Similarly, electric fields and magnetic fields are facets of the same field called an electromagnetic field. This field is described with an electromagnetic field tensor.

A reference frame moving with respect to the charge and a reference frame stationary with respect to the charge are related by a hyperbolic rotation. And so people in the different reference frames will see different facets of the electromagnetic field, analogous to the different facets of a rubik's cube.

This is why the trajectory of an electron will bend in the presence of a magnetic field. From our stationary perspective, we only see a magnetic field. But from the electron's "hyperbolically rotated"/moving perspective, there is also an electric field and hence the electron is affected by the electric field.

Similarly, a generator works by moving a magnet across a coil of electrons. Even though the magnet only has a magnetic component to its field, by moving it, we are "hyperbolically rotating" its electromagnetic field so that the electrons will see an electric field and hence travel through the coil, generating electricity.

FISMA

Morbert wrote: »

If we are facing a rubik's cube from different angles, we will see different colours, as each colour is on a face of the complete cube. And if the cube is rotated, or if we rotate out positions, we will see a different combination of colours again. Similarly, electric fields and magnetic fields are facets of the same field called an electromagnetic field. This field is described with an electromagnetic field tensor.

Nice analogy, I will remember to cite "Morbert" whenever I use this!

Slan.