How is potential difference maintained in a battery? I am beginning of learn electricity so sorry if my questions are confusing or does not make sense. My question is specifically about how voltage (which I guess is due to separation of uneven charges) is constantly maintained in a battery. My knowledge of battery comes from chemistry and there examples of battery were not as complicated as those found in physics. Like in chemistry we learned of how electrons traveled one one electrode to another another and when the charges are evened the battery then dies. But in physics I am reading of examples when the battery constantly maintains the voltage and charges keep on traveling the circuit even when they reach the other terminal. Can anyone explain how this is happening? I guess I don't understand how batteries work completely.
 A: So technically, in those physics examples the voltage isn't fixed in those batteries. The potential drops, just very slowly for small currents. For example, if the voltage is 12V and some small current flows, the voltage drops. However, it drops to like, say, 11.9999935434V or whatever. So for the problem you don't really care and you just assume 12V. Eventually, once the current has run long enough it will become noticeable in practice that the voltage is not 12V. And that's when you need to recharge the battery (if rechargeable) or get a new one.
A: 
My question is specifically about how voltage (which I guess is due to separation of uneven charges) is constantly maintained in a battery.

The battery voltage is maintained due to a multitude of chemical reactions within the battery that maintain separation of charges. But batteries only have a finite life as the chemicals within the battery will run out eventually.

But in physics I am reading of examples when the battery constantly maintains the voltage and charges keep on travelling the circuit even when they reach the other terminal.

The reason the electrons are able to travel around the circuit is because there is a potential difference between each subsequent infinitesimal segment of wire.
Or put in another way each part of the wire is at a slightly higher potential than the subsequent adjacent part. If you think about this it would have to be the case as the electrons can never flow around the circuit without a potential difference.
Very loosely speaking; Potential Difference drives current.
If you connect a 9V battery to a circuit without any components. The 9V battery means that each Coulomb of charge has 9 Joules of energy acquired from the battery; and this energy must be dissipated in the circuit wires, since there is no resistor, thermistor, or LED etc. for each coulomb of charge to transfer its energy to. 
So the only thing that can happen is that the circuit wires will heat up since the energy acquired by each coulomb of charge from the battery must be transferred somewhere, and so the 9J per coulomb will all be transferred to the circuit wires. You probably know this as it is more commonly referred to as a "short circuit".  
