A battery with internal resistance r is connected to a load resistance R. If R is increased, does the terminal voltage of the battery increase, decrease, or stay the same?

The terminal voltage of the battery decreases.

Explanation:

An idea battery does not have internal resistance but a real practical battery always have an internal resistance r connected in series with the battery.

This internal resistance causes a voltage drop when load R is connected, a current I flows in the circuit which causes a voltage drop I*r in the battery therefore, the terminal voltage of the battery will decrease.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach