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It is well known that moving charge generates magnetic field. But as far as I understand it mostly relates to current type of movement. For example, if I take plastic rod and rub it with fur (to negatively charge it) and then wave the rod, I will not generate magnetic field. Am I correct?

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If you wave a charged rod, you will indeed generate a time-dependent magnetic field. In fact, as the field is time-dependent, you will not only generate a magnetic field but also an electric field, the two of them forming an electromagnetic wave propagating away from the rod. It is true that this em wave will be of very low energy, but nonetheless it will be present.

We can make a rough estimate of the amplitude of the magnetic field. I believe that rubbing a rod builds up a charge of the order of nanoCoulombs ($10^{-9}$C). Let us say you are shaking the rod (vigorously!) at 10 Hz. This will give rise to a current of the order of 10 nA. The magnetic field at a distance $r$ from a straight wire carrying a current $I$ is given by: $$I = \frac{\mu_0 I}{2 \pi r}$$

So 1 cm away from the rod, the magnetic field will have a peak value of about $10^{-13}$ T. This is extremely low - as a benchmark the magnetic field of the Earth is about $10^{-5}$T, so it is about 8 orders of magnitude lower than that. I doubt that this will be measurable, except maybe by a SQUID.

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  • $\begingroup$ Only very, very little radiation will result. $\endgroup$ – my2cts Feb 19 at 15:25
  • $\begingroup$ Thank you very much! As far as I understand electric field will be present even without moving the rod. How can I conduct an experiment to detect this magnetic field? Were there any experiments done to detect it? $\endgroup$ – user1700890 Feb 19 at 16:19
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    $\begingroup$ I've added an estimate of the size of the magnetic field to the answer. $\endgroup$ – Clara Diaz Sanchez Feb 19 at 17:14
  • $\begingroup$ Thank you very much for the estimate! I am thinking that I can replace plastic rod with some greater charge (capacitor) and then conduct an experiment. $\endgroup$ – user1700890 Feb 24 at 20:42
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But as far as I understand it mostly relates to current type of movement.

Yes. The charges are moving when you wave the rod. And current is nothing but moving charges.

And this current causes a magnetic field.

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    $\begingroup$ If the rod is charged, moving the rod around will definitely generate a magnetic field. $\endgroup$ – Mauricio Feb 19 at 15:18
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    $\begingroup$ @Mauricio I did not agree to there being no magnetic field. I agreed to the statement of magnetic field being a resultant of currents. But yes. My answer at the first glance was misleading. So I have edited to make it more explicit. $\endgroup$ – Superfast Jellyfish Feb 19 at 15:21
  • $\begingroup$ @Mauricio, but why? Magnetic field is a result of electron (or charged particle) spin and orbit alignment. Moving charged rod does not change electrons' spin or orbit. $\endgroup$ – user1700890 Feb 19 at 16:21
  • $\begingroup$ @user1700890 imagine that you move the charged rod in a rigid circular fashion, it would be analogous to an electric charge in a circular orbit, thus creating a magnetic field $\endgroup$ – Mauricio Feb 19 at 16:29
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    $\begingroup$ @user1700890 no experiment comes to mind, but maybe if you can put a strongly charged object in some spinning wheel connected to a motor, all that next to a compass, you should be able to see the compass needle move when you accelerate the wheel. Nevertheless I still wonder if the field would be strong enough. $\endgroup$ – Mauricio Feb 19 at 16:52

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