I am trying to understand some facts on electrical potential and potential energy. It is quite confusing in the text to say that the zero potential could be freely chosen for convenience. In that case, how do you interpret the associated energy and the sign.
Let me start with the gravitational energy as analogy. Let's said I am standing on a high platform H h meter above the ground. If I am free to chose where the zero potential is, I consider the following two cases:
1) Assuming the ground has zero potential energy, the potential energy that I have is $mg(H-0)=mgH$. This makes sense to me since I have positive energy since I am standing in high place and I have potential to fall if I jump so my positive energy will convert into kinetic energy.
2) But what happens if I choose the zero potential at where I stand so the ground is at $-H$, so my energy is $mg(-H-0) = -mgH$, so is that negative really mean? I can only have one specific energy because I am standing at one place. So how does this negative potential energy related or equal to the positive one at 1)?
Now come to my question on electrical potential and energy, it is even more confusing because we have two different kind of charge (positive and negative). Let's consider the following case
Two metal terminals are connected to a battery (voltage is $V$). If I have an electron between the terminals, what is the potential energy the electron experience? As I learn from the text, the electrical potential energy should be $qV$, where $q$ is the charge of the particle, $V$ is the potential difference. Again, if we are free to choose the zero potential point, it may end up with two potential energy
1) By choosing the negative terminal as zero potential point so the potential energy for the electron should be $-e(V-0)=-eV$, which is negative. This makes sense to me because a negative charge will move away from the the negative terminal instead of the positive one, so it has negative potential energy (it won't move by itself towards the negative gate).
2) By choosing the positive terminal as zero potential point so the potential energy for the electron should be $-e(0-V)= eV$. It is hard to understand what is this positive potential really mean.