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In a closed circuit, electrons flow from negative electrode to positive electrode.

In an open circuit, electrons only flow up to the end of the circuit.

Why don't the electrons keep flowing into the vacuum until the negative electrode on the battery drains off electrons ?

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If you think about the flow of electricity at the atomic level. The electrons flow by changing the positions from one atom to the other from their valance shells.

The battery just provides the electromotive force or the electric field for the movement of the electrons in the conductor. it is due to the interaction of the electron with this field.

The free electron theory in metals will give you a great idea about the topic. The negative electrode will not contain the electrons but the electro chemical reaction causes the electron to flow and complete the circuit.

The electron may come out of the conductor tip even if the battery is not there by the effect of photoelectric effect. But the work function for that material is what determines whether the electron will flow in the vacuum.

And to give a precise answer to your question the dielectric constant of vacuum is a lot.

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You have to supply some energy to let electrons leave a solid, this energy is called work function; if the work done by the battery is less than the work function then the electrons cannot flown into the vacuum.

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in an open circuit electrons do not flow like in closed. If electrons leap out in space battery will get positively charged and will prevent electron from escaping. in closed circuit there is no net charge on battery.

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