Everybody knows you can produce electrostatic charge rubbing two different materials together. But have you ever smelt e.g. at the plastic after charging it? There actually is a distinct electrostatic charge smell 🙂 While normally smelling involves the transport of molecules, what you are smelling here, is the electric field itself, or do you? What is happening?
[Physics] Where does the smell of electrostatic charge come from
electrostatics
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I've never done the experiment with the plastic film, but as child I remember that if I rubbed a balloon on my pullover it would stick to the wall. The reason is the one you suggest. When you run the balloon on your pullover you charge it. When you bring the balloon close to the wall the charge on the ballon polarises the surface of the wall, i.e. it repels like charges and attracts unlike charges, so the surface of the wall acquires a charge opposite to the balloon. The opposite charges on the ballon and the surface of the wall attract, so the balloon sticks to the wall.
The problem with using this to fix pictures to the wall is that the charge gradually leaks away so the balloon/picture will fall off. My recollection is that the balloon would stay stuck to the wall for about an hour.
As you say, objects may be charged by rubbing them and this is called triboelectricity. Alternatively you can charge objects by touching them with something else that is charged. Because like charges repel, if you touch a charged object to an uncharged object there will be a tendancy for the charge to spread over both objects. To what extent this happens depends on the conductivity of the objects. I imagine the plastic film is a poor conductor and this is why you have to rub the Fun-Fly-Stick all over it.
I had never heard of the Fun-Fly-Stick but a quick Google suggests it's a type of Van de Graaff generator.
First, an electron has both an electric charge -e and an intrinsic magnetic dipole moment N-S, μ.
Static electricity in the needle means that you rearrange the charges in the needle and you spatially split them in negative region (one end of the needle) and positive (other end of the needle). Negative region is the region which has an excess of free electrons where positive region is the region which has a lack in the number of electrons. This charge imbalance causes the electrostatic charge and field of the needle when rubbing it with a cloth.
However in this kind of charge the magnetic moments of the electrons are randomly scattered in any direction therefore there is no magnetization of the needle thus it CANNOT SENSE and respond to the magnetic field of the Earth.
Magnetostatics are different. Charges (i.e. electrons) are evenly distributed inside the matter of the metal needle. If you can find a way assuming the needle material is ferromagnetic to re-orient all magnetic moments of the unpaired electrons to align to the same direction then you will magnetize the needle and it will sense the magnetic field of the Earth and needle will respond by aligning to the magnetic field of the Earth!
See below illustration of the difference between electrostatically charged matter and magnetically dipole charged matter (i.e. magnetized):
Green arrows represent the magnetic moments N-S direction of the electrons.
It all depends on the material if it is magnetizable or electrostatic chargeable? There are materials that respond both to magnetic and electrostatic charging but eletrostatically charging a material will not make it magnetic and magnetizing it will not make it electrostatic.
Note: Even, when uniformly rubbing the needle with a cloth so that you end up with a uniformly electrostatically charged needle (i.e. the whole needle surface lacks in electrons or has an excess of electrons relative to other material objects), it will still have its charges' magnetic moments randomly oriented and therefore you cannot achieve magnetization of the needle by triboelectric effect. Electrostatic charging is about spatially transferring whole charges from one place to the other. Magnetostatic charging is about turning the charge's magnetic moments so that they face all to the same direction. It's two different things which each requires a different procedure to be accomplished assuming the specific material's atomic structure allows it.
Update 22 Nov 2021:
Although the above answer is describing the general case farther investigation revealed this article I cannot dismiss lightly since in almost every rule there are exceptions and we must be open minded:
Survival Gear: How To Make A Compass
It says: "you can magnetize a needle by rubbing it against your hair, some animal fur, or silk. Carefully hold the sharp point of the needle and rub just the eye of the needle 50 to 100 times against the hair, fur, or silk."
In first glance this may seem ridiculous but there is possibility to both electrically charge in this case the needle and also magnetize it!
This is because it says to only rub the eye, the very tip of the needle. It is possible in such as small volume (less than a few microns cross-section) the electrostatically accumulated charges in there to end up also more or less with aligned magnetic moments in the same direction. Therefore aligned magnetic domains are formed at the very tip of the needle that would act as a magnet.
Only an actual experiment can tell with the needle seeking the Earth's magnetic south pole (i.e. located close to the Geographic North pole).
I expect this magnetization effect to be very small, if any at all, but a needle floating on water, could work.
Update 26 Nov 2021:
I did an experiment linked on the comments below (please read also my related comments below addressed to @Ed Flea, to avoid any misunderstandings). Nothing conclusive unless repeated many times and replicated also by others, although it seems at first glance a positive result.
Update 28 Nov 2021:
Okay, I have repeated this experiment many times now and my results show conclusively that you CANNOT magnetize the eye of a needle by static electricity (i.e. triboelectric effect) as some of these survival guides magazines claim.
The first experiment run I've got a positive result must have been a fluke, somehow accidentally the needle must have been magnetized. I bought some new needles and repeated the experiment 10 times, always with the same result. No magnetization of the needle.
Conclusion: You cannot magnetize a needle by static electricity.
Best Answer
You smell ozone ($\mathrm{O_3}$, from the Greek word ozein for "smell"), and maybe nitrous oxide - the reaction product of oxygen and $\mathrm{N_2}$.
There is a nice description of the formation and action of ozone at this link. Briefly:
Oxygen molecules ($\mathrm{O_2}$) can be dissociated (broken into atoms or ions) by either UV light, or electrical discharge. The resulting radicals are extremely reactive, and will react with other molecules. Reacting with oxygen, they will form ozone; reacting with nitrogen, they will form nitrous oxide. When you inhale ozone, it reacts with the water in your nose and forms hydrogen peroxide. The combination of that, and the nitrous oxide, is what you smell near photocopiers (which, if they use the Xerox process, operate with a high static voltage inside) or anywhere that you have high voltages and corona discharge (as you will get when rubbing dissimilar insulators together).
It's possible you also smell other things - but ozone is the one that is always present (you can sometimes smell it as a thunderstorm approaches, as the local electrical field builds up and small discharges occur ahead of a lightning strike. While this process occurs at higher altitudes, the approaching thunderstorm is associated with vertical air currents and this transports ozone from higher altitudes to ground level.) See for example this Scientific American article