# A Magnetic field of moving charges

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1. Oct 25, 2016

### samueljun

Hi! I wonder if there was any experimental measurement of magnetic field produced by mechanically moving charges.

In principle the equation is well known.
(1)

But is there any experimental proof of this equation? I know it can be reformulated into this.
(2)

My question is "Is there any experimental proof of Eq. (1)?"

I guest particle accelerator level experiment would create detectable magnetic field. I read lightning magnetise things, but it is not a direct measurement.

Please let me know if there is any DIY level experiment of measuring magnetic field by mechanical movement of charges. If it is not possible, could anyone explain why?

Thank you in advance!

2. Oct 25, 2016

### Staff: Mentor

What do you count as mechanical movement? Is an electron beam okay? In that case: not hard to detect.

Moving a solid object with a net charge produces tiny magnetic fields. Moving a 1µC charge by 1 km/s (that is a bullet) leads to a field of ~10nT at a distance of 10cm. Detectable, but not as DIY experiment.

3. Oct 26, 2016

### samueljun

Thank you mfb. Could you give me any reference that measures magnetic field of electron beam? I see only articles of electron beam deflected by magnetic field.
By the way, I found this article.
http://educate-yourself.org/cn/ElectronBeamMagneticField.pdf
This says that magnetic field is not due to the eq. 1 of my post but to intrinsic magnetic moment.

4. Oct 26, 2016

### Staff: Mentor

I'm not aware of dedicated measurements (they probably exist, but searching for them is basically impossible, you get spammed with results of deflecting a beam with external fields), but some linear accelerators can produce beam currents larger than 100 mA. A simple hall probe next to the beam would be sufficient.

In colliders, the electromagnetic field of one beam has a significant impact on the other beam. This is called beam-beam effect and well studied.

5. Oct 28, 2016

### samueljun

Many thanks to mfb. I wonder if the water drop levitating (orbiting) effect of Kelvin Generator can be the example of magnetic field formation by mechanically moving charge. Otherwise it is so strange.... Please have a look at the videos.

Kelvin dropper experiment is easy to set up. The reason for water drop splashing is charged water repulsion. But orbiting around the ring with static electricity is not easy to explain. The only way is that the magnetic field direction changes with time so that the electric field is induced.

I look forward to your great opinion!

6. Oct 28, 2016

### Staff: Mentor

Orbiting around the ring is exactly what you would expect with a simple quasistatic electric attraction.