Yes, all materials have an electrostatic charge unless you define 'charge' as potential difference between two or more points.
The object is to create a difference in charge and then make that into usable current.
Having a conductive disk holding the target charge is a problem due to the eddy currents created when that charge is moving.
So, the solution would be to have charge instead held by a dielectric and the conductive plates have no relative motion to the changing magnetic field.
What I'm looking for is previous works showing potential difference created within a dielectric (and therefore, the capacitive surfaces sandwiching that dielectric) by means of applying a changing electromagnetic field.
Some work exists but it is questionable - ex. FTL toroidal capacitor bending/warping space-time. The term 'toroidal capacitor' usually leads to Sci-Fy movies, the old use of the term for measuring current in a conductor or somewhat wacky research into FTL travel.
The inverse of Lorentz's moving charge in a magnetic field should be easily found (static charge in a changing magnetic field).
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