Electricity is the movement of electrons from one atom to another or the movement of charged negative particles (ions)?
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An electric current is the flow of electric charge. But electric charge is not an entity, it is a property that must be 'carried' by a charge carrier.
An electron current, the flow of electrons, contributes to an electric current since the electron 'carries' negative electric charge. However, an electric current is not necessarily an electron current.
The flow of ions (either positively or negatively charged) also contributes to an electric current in, for example, the electrolyte of an electrochemical cell.
As an aside, electricity is not identical to electric current. From the Wikipedia article "Electricity":
Electricity is the set of physical phenomena associated with the presence and flow of electric charge.
Alfred Centauri
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