# To which extent cathode rays can be considered as current in a wire

1. Feb 17, 2012

### universal_101

I want to know if there is magnetic field around a cathode ray tube. That is, does magnetic compass deflect when brought close to a CRT ? If so, can this magnetic field (produced by cathode rays) be used to have Lorentz force on a moving charge particle ?

Presently, what I think is,

Maxwell's equation, $c^{2}\nabla \times B = \frac{j}{\epsilon_{o}} + \frac{\partial E}{\partial t}$

Demands the need of Magnetic field for cathode rays, and the Lorentz force then should put some force on the nearby moving charge. But, due to relativity this magnetic force is balanced by extra electric force due length contraction.

Is that so ?

2. Feb 17, 2012

### Staff: Mentor

A cathode ray is a current, but it isn't a current in a wire. The current can do all the things you would expect of a current in EM, including producing magnetic fields.

The only thing is that if there are any external fields it will pretty easily re-shape the current, that is the big difference from a current in a wire which tends to stay in the shape of the wire.

3. Feb 17, 2012

### ZapperZ

Staff Emeritus
Note that devices such as an Intergrated Charge Transformer are often used in accelerators to quantify the amount of charge moving in an accelerator beampipe. This is nothing more than a coil of wire to pick up the magnetic field from the moving charges.

So the properties are practically similar.

Zz.

4. Feb 17, 2012

### harrylin

The first point has already been answered. The remaining point:
I don't think so: Maxwell's description is supposed to be valid in the "stationary" system to which you refer. "length contraction" suggests the use of another inertial system that is in motion relative to your "stationary" system, but to which you not refer.

5. Feb 17, 2012

### universal_101

The frame in which length contracts is the one in which there should be magnetic force due to motion of the charge particles of cathode rays.

6. Feb 17, 2012

### universal_101

Thanks, and for using the great example.

7. Feb 17, 2012

### harrylin

I would not know what length would contract: in your description I discern no object of fixed length on which that concept can be applied.
And independent of such considerations, the magnetic force and electric force are already given by the equations of Maxwell.

PS. concerning the question in the title: an important difference is that a cathode ray is strongly charged while a current in a wire is electrically neutral.

Last edited: Feb 17, 2012
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