as the title states... how does one do such thing? oscillating electric field induce magnetic field. oscillating magnetic field induce electric field.
all these experimentation I've read is that of electrical currents and permanent magnets but yet to see one done with electrostatic.
There is no magnetic field around a stationary point charge. However, if you were to set this charge in motion, then there would be a magnetic field because a magnetic field is produced by moving charges or current.
From Wikipedia's article on electrostatics (emphasis mine),
...electrostatics does not require the absence of magnetic fields or electric currents. Rather, if magnetic fields or electric currents do exist, they must not change with time, or in the worst-case, they must change with time only very slowly. In some problems, both electrostatics and magnetostatics may be required for accurate predictions, but the coupling between the two can still be ignored. Electrostatics and magnetostatics can both be seen as Galilean limits for electromagnetism.
The coupling referred to here is the Maxwell's equations: (specifically Faraday's law and Ampere's law): \begin{align} \frac{\partial\mathbf E}{\partial t}&=c\nabla\times\mathbf B\\ \frac{\partial\mathbf B}{\partial t}&=-c\nabla\times\mathbf E \end{align} (using Gaussian units here).
What the quote I gave at the beginning is saying is that, because electrostatics means there is no time-varying field, the one field being induced from the other cannot actually happen as you've requested, simply because of the definition of electrostatics.
What makes you think is possible? Is like asking for current but with stationary charges and when I say stationary charges I don't mean stationary current. Literraly nothing moves and you want current. Is like some broken perpetum mobile ideea tbh. Don't take it too personal but there can't be a magnet that raise from electrostatics. In fact, if you try to imagine a gedanken experiment, if you sit on a moving charge you will never be able to measure a magnetic field. So nop, if you are stationary to the charge there is no magnetic field for you.
Magnetic fields are induced by currents and by time-variation of electric fields. Electrostatic fields aren't currents or electric fields (neither the hypotetic magnetic monopoles)... so they don't produce magnetic field. The answer is in the Maxwell equation.
(To HolgerFiedler: the electrons in their static orbits have angular momentum, so they produce currents. In QM, currents don't need "velocity")
Quote from the answer from programmingenthusiast:
There is no magnetic field around a stationary point charged.
This is right for a charged sphere but not for single electrons. They obey the intrinsic property of a magnetic dipole moment and this is nothing else as a magnetic field. In permanent magnets some electrons aligned all in the same direction, building a macroscopic magnetic field.
How does one induce magnetic field through electrostatic?
Some materials are natural electromagnets. To make a strong permanent magnet one has to use compounded such like rare-earth elements:
Rare earth (lanthanoid) elements have a partially occupied f electron shell (which can accommodate up to 14 electrons). The spin of these electrons can be aligned, resulting in very strong magnetic fields,...
You have to mill such materials into powder and press them together under temperature (sintering)[https://en.wikipedia.org/wiki/Sintering] and in a strong external magnetic field. After cooling down you get “freezes” electrons, all of their magnetic dipole moments aligned. At least, be careful not to drop such a magnet, it will bursting in pieces.
