Why are the potentials the same?

[s3a]

Could someone tell me why the potentials are the same in http://i.imgur.com/EdnqE.jpg.

I am talking about right under the part where it says "Also, the potentials across them are now the same, so that V = q/C gives". I understand everything prior to that. I even understand the stuff after it! I just need to justify to myself the theory behind why the potentials are equal so that I can move on. Please be elaborate but a short response is fine.

Any input would be greatly appreciated!
Thanks in advance!

 

[rock.freak667]

They are connected in parallel so the potential is the same for both.

 

[s3a]

How do you discern that they are parallel? I was under the impression that "(b) After" is in series.

 

[rock.freak667]

The positive terminal is connected to the positive terminal in both capacitors.

 

[rwisz]

The reason why the potentials are the same in the given image is due to the principle of conservation of energy. This principle states that energy cannot be created or destroyed, only transferred from one form to another. In this case, the energy in the system is electrical potential energy, which is dependent on the charge and distance between the two plates.

Initially, the two plates have different charges, with the positively charged plate having a higher potential energy than the negatively charged plate. However, as the charges move towards each other and eventually reach equilibrium, the energy is transferred from the positively charged plate to the negatively charged plate. This results in both plates having the same potential energy, as the total energy in the system must remain constant.

Furthermore, the potential difference between two points is defined as the change in potential energy per unit charge. Since the charges on both plates are the same, the potential difference between them must also be the same. This is why the potentials are equal in the given image.

In summary, the equality of potentials in the given image can be explained by the principle of conservation of energy and the definition of potential difference. This concept is crucial in understanding the behavior of electric fields and circuits, and is a fundamental principle in the field of physics. I hope this explanation helps to clarify the reasoning behind the equality of potentials in the given image.