Water doesn't flow in the pipe when (a) both ends are at the same level. Another way of saying this is that water will not flow in the pipe when both ends have the same potential energy (PE).
Similarly, charge will not flow in a conductor if both ends of the conductor are at the same electric potential.
But tip the water pipe and increase the PE of one side so there is a difference in PE across the ends of the pipe, as in (b), and water will flow.
Similarly, increase the electric potential of one end of an electric conductor so there is a potential difference across the ends, and charge will flow.
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