# Graviational vs Electrical Potential

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1. Oct 30, 2015

### Novanglus

Hi all,
Thanks for taking your time to help me. It means a lot!
For some context: I'm a physics student taking an analytical chemistry course and am a bit confused by the concept of electrical potential.
Gravitational potential is the potential energy per unit mass, V(gravitational) = U/m. (I think) this means that the gravitational potential of an object on top of a mountain is higher than the V(g) of that same object near the ground. Therefore, objects spontaneously move from a higher V(g) to a lower V(g) and they lose energy while moving therefore having a negative change in energy.
In electrical potential, V(electrical) = -nF∇G where n is number of electrons, F is faradays constant, and G is change in free energy. The units are J/C. I'm confused because in this system, electrons travel spontaneously from a lower potential to a higher potential. This is the direct opposite of gravitational potential (if Im understanding everything correctly). Could someone explain why there is this difference using math or words?
When I think about it conceptually, I get further confused: As electrons are moving through a circuit, the circuits voltage (aka electrical potential) determines the amount of energy each electron, in other words, each electrons capability to do work. As the electron moves through the circuit, it loses energy until it reaches the other side. So it seems that the electron is moving from a higher potential to a lower potential. Whats going on here?

2. Oct 30, 2015

### sophiecentaur

Is there a problem here? Potential energy is lost in both cases. The unit test mass corresponds to the unit test Positive Charge. Forget about electrons - just think in terms of Charge (positive).

3. Oct 31, 2015

### Chandra Prayaga

The confusion arises because you are trying to formulate a universal rule, and making a mistake in doing so. It is not true that in all cases, there is a force on a particle pointing towards lower potential. The correct statement is that there is a force pointing towards lower potential energy. This last statement is true in both gravitational and electrical situations, and it is also true for negative, and positive charges. That is why positive charges move toward lower potential, which means lower potential energy for them, and negative charges move towards higher potential, which means lower potential energy for them.

4. Nov 2, 2015

### Novanglus

Ok, I think I am starting to understand what you mean. This was a great way of putting it. But I don't see this appearing in the equation for electrical potential.
V = -nFΔG​
There is no where in the equation where you would assign the charge of the particle therefore changing the sign of potential. All that changes the sign is whether change in Gibbs free energy is positive or negative. For a battery with a positive voltage (learning about galvanic cells), the reaction must be spontaneous from left to right (anode to cathode).
Are you saying if it was positively charged particles flowing instead of electrons that they would flow from the cathode (higher standard electrical potential) to the anode (lower standard electrical potential) and therefore be flowing from higher energy per unit charge to lower energy per unit charge?
Is there a way to account for the charge in the equation? Or is the whole equation crafted on the assumption that it is electrons flowing? And if so, how far back in the derivation of electrical potential do you have to go to see where that assumption is made?
If anything of what I am writing is confusing, please let me know and ill try to rephrase. It all makes sense in my head, but I can definitely imagine someone else reading this and thinking "what in the world is this dummy thinking?"
Thanks again!

5. Nov 2, 2015

### Chandra Prayaga

A figure would have been nice, to clarify what is left and right. Anyway, an equation for a potential cannot have a specific charge (positive or negative) in it. There is nothing called one potential for positive charges and one for negative charges. The potential of a battery is determined by whatever chemical processes are going on inside the battery. Once the potential is fixed, the positive terminal of the battery is always at a higher potential than the negative terminal. This has nothing to do with what charge is moving where.

1. You could use the battery to generate current in a metal wire, in which case electrons would move from low potential to high potential, and therefore from high potential energy to low potential energy.
2. You could use the same battery to do electrolysis, or generate current in an overall neutral plasma, in which case, you would have both kinds of charges moving. Electrons or negative ions would move from low to high potential, and positive charges would move from high to low potential, and, as I said earlier, BOTH would be moving from their respective high potential energy to low potential energy.

In all cases, the battery would have the same potential difference, with positive terminal at high and negative terminal at low potential.

6. Nov 2, 2015

### Novanglus

But don't you see the disconnect there? Potential is described as potential energy per unit charge. So if a particle is moving from a state of high potential energy to a state of low potential energy (as in any spontaneous reaction) then the electrical potential should ALSO have a negative change:

ΔU = U2 - U1 = some negative number (where U = potential energy, and reaction is assumed to be spontaneous)
ΔU/C = U2/C - U1/C = some negative number (where ΔU/C is defined as potential)
In order for ΔU/C to be positive, C (coulombs) must be negative. This doesn't happen in gravitational potential because m (mass) is always positive.​

7. Nov 2, 2015

### Chandra Prayaga

There is no disconnect. If you actually put in the correct value for the charge C in your equations, you will see the point. Here is a numerical calculation:

The battery has a potential of 1.5 V. Call the positive terminal as + and the negative terminal as -. The battery ALWAYS gives: V+ - V- = 1.5 V
The battery does not have one potential for electrons and a different potential for protons.

So the potential energy difference of an electron when it is at each terminal is:
Ue+ - Ue- = - e (V+ - V-) = - e (1.5V) = - 1.5 eV

For a proton:
Up+ - Up- = e (V+ - V-) = e (1.5V) = + 1.5 eV

8. Nov 2, 2015