Electricity flows when charged particles move from areas of high concentration to low concentration. Once all those particles have moved, the flow stops. The fluids inside and outside our cells have different concentrations of charged partials. This has the effect of causing an electrical charge between the inside and outside of the cell. In order for electricity to flow, the ions need a way to flow in and out of the cell. However, there is a cell membrane in the way that prevents the ions from flowing between the two. It does happen though. This happens in a controlled manner to let neurons fire and ions essentially leak in and out of the cell during other biological processes. Our cells have molecular pumps and valves to move ions around to create or maintain charges.
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