According to my book (and various other sources), the salt bridge in a galvanic cell serves to keep the solution electrically neutral. Yet I was not able to find any information on why the solution needs to be electrically neutral. As long as the oxidation reaction takes place in the anode (thereby dumping electrons and rendering the anode negatively charged) and the reduction reaction continues in the cathode, the charge disparity should create a potential difference right?
What happens when the solution isn't electrically neutral that prevents the oxidation and reduction reactions from taking place, because if they were taking place the electrodes should have a non-zero potential difference right?
So my question basically is, why does the electrolytic solution need to be electrically neutral in order for a potential difference to develop between the electrodes of a galvanic cell?