How do nerve cells work

The charge on the inside of a cell is negative with respect to the surrounding solution. A potential difference of about —70 mV forms across the axon (cell membrane) when the cell is at rest , i.e. before passing an impulse - we sometimes call it a rest potential, which is caused ultimately by differences in concentration either side of the axon (membrane). 

Movement of charge across the membrane causes the potential to change. A huge difference in concentration is seen in composition between the inside of the axon and the remainder of the nerve structure. For example, consider the compositional 

No potential difference forms along the membrane surface, only across it. 

Cell exterior to separate the cell interior and exterior 

Source J. Koryta, Ions, Electrodes and Membranes, Wiley, Chichester, 1991, p. 172. 

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