Open circuit in a constant electric field In the figure, an external wire is "tapped" into a box inside which exists a constant electric field whose direction is from left to right. The wire does not touch the wall of the box, i.e., the wire is not closed.
From my understanding, charges inside the wire will move within the wire from one end to the other until the potentials of the two ends are equal. After that, there will no current in the wire.
However, it looks like a contradiction to me because the electric field inside is maintained constant, which means the two ends of the wire cannot have the same potential.
Could you explain to me what I am missing here?

 A: Using $V_1=E_1\cdot l$, where $l$ is the length between the wires we can find the voltage difference of the two ends where $E$ is maintained constant.
Since there is a potential difference between the two ends, charges will flow, but since the loop is NOT closed, the question if till when will the charges continue to flow.
Remember that a wire has only a finite number of electrons and a wire cannot create more electrons, meaning if the flow is not sustained it has to stop at some point in time. Hence, the question when does that happen.
The accumulation of electrons at one end and positive charge at other end will eventually lead to a creation of electric field of exact same magnitude and opposite direction, but inside the wire. Now, you can picture this as a second electric field $E_2$ through the wire, or for that matter between the two arms but outside the box of constant electric field (just thing of the opposite charges being accumulated at each arm of the open circuit).
This accumulation stops when $E_1=-E_2$ which means that $V_1=-V_2$ or $V_1+V_2=0$. Hence no potential difference and charges stops flowing.

Its a different story if you also account for the capacitance of the wire in which case the charges keeps oscillating until it gets dampened and reaches the equilibrium state of $E_1=-E_2$.
A: Current will continue to flow and charge will continue to accumulate on the ends of the wire.  Eventually a tremendous charge difference will result.  This charge difference will create an electric field that counters the original field.  More and more energy will have to be added to the original field to kept it constant and uniform.  At some point the energy required will become larger than any amount that may be available and the field inside the box will no longer be able to be kept constant.
In the real world the charge difference on the wire would probably eventually cause an arc to occur and then the wire could not be considered to be an open circuit.
