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A single moving electrical charge creates a magnetic field.

Changing magnetic field creates eddy (electrical) currents (Foucault currents) in conductors only.

But how changing magnetic field influences a single electrical charge, say electron?

Textbooks write that magnetic field has no influence on a charged particle if that charged particle is not moving (moving with respect to what? To reference frame in which I make observations? So in one reference frame influence would exist and in another - won't, even if we have same electron and same magnetic field?) - so may I derive from that that a changing magnetic field has no effect on a charged particle (electron) that is not moving in my reference frame where I observe it? Or the fact that magnetic field is changing can exert effect on a non-moving electron?

Changing magnetic field creates eddy currents in conductors, but if we have a current - we have difference of potentials (or another correct term: electromotive force, voltage) - but definitely it is something that makes electrons move, so this is some force acting upon electrons - so does changing magnetic field exert any effect on a single resting (not moving) electron / charged particle? If not, why changing magnetic field does exert effect on every single electron (=> and thus on a single electron)?

This SO answer states that changing magnetic field imparts a force on a stationary charged particle.

Also, is it correct to reason like this: changing magnetic field always produces electrical field, and that electrical field definbitely exerts influence even on stationary charged particles?

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It seems like your answer is in your question. You know that a changing magnetic field produces an electric field. Electric fields can act on stationary particles. So yes, a changing magnetic field can influence a single particle through the resulting electric field.

In regards to your text book quote, they are probably talking in the context of magnetostatics, where currents producing the magnetic fields in question are assumed to be constant, so the magnetic field is not changing. When they talk about charges at rest they mean with respect to the field. So if I see an electron in a constant (in time) magnetic field at rest, then I know it will not experience a force from that magnetic field.

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