# Doubt regarding Notations for potential difference in EMFs

Possible source of confusion -For work done carrying a unit charge from Point 1 to Point 2, ie the Potential difference, is it

Voltage, $$(V_{21}\:)=V_2\:-V_1\:$$

OR is it

Voltage, $$(V_{12}\:)=V_2\:-V_1\:$$

Secondly, when we talk about the potential difference between $$A$$ and $$B$$, do we mean work done carrying a unit charge from $$A$$ to $$B$$ or the other way round. Is it equal to $$(V_{AB}\:)$$ or $$(V_{BA}\:)?$$

if you answer these alone, I would be very grateful!

Longer story, aka the inspiration...

...The positive electrode has a potential difference $$V_{+}\:$$ $$(V_{+}\:> 0)$$ between itself and the electrolyte solution immediately adjacent to it marked A in the figure. The negative electrode develops a negative potential $$–V_{-}\:$$ $$(V_{-}\:> 0)$$ relative to the electrolyte adjacent to it, marked as B in the figure. When there is no current, the electrolyte has the same potential throughout, so that the potential difference between P and N is $$V_+\:-\left(-\:V_-\:\right) = V_+\:+\left(\:V_-\:\right)$$ . This difference is called the electromotive force (emf) of the cell and is denoted by ε.

Can any one help me trace the path of the positive charge in this case and give a better definition of $$V_+$$ and $$V_-$$ in this case along with 2 things. The fact that both are defined as positive annoys me, maybe it could be a typo.

1. The path of the positive charge in those $$V_-$$ and $$V_+$$
2. Mathematical representation of in the form format $$V_-$$ = $$V_{NB}$$ = $$V_N$$- $$V_B$$ or whatever is actually correct

## 1 Answer

(a) I'd take $$V_{21}$$ to mean $$V_2-V_1$$, that is the potential of point 2 relative to point 1. But I think that the user of the $$V_{21}$$ notation ought to explain how he or she is using it – it's probably not wholly standard notation.

(b) I don't think that there's any agreed convention about the sense of "the potential difference between A and B". If I wanted to use the phrase I'd say something like "the potential difference between A and B is 6.0 V, with A at the higher potential."

(c) Perhaps your annoyance with the $$V_-,\ V+$$ notation might be lessened if you think about these as the magnitudes of the potential differences at the two electrodes.

• interestingly i found this which says "The electric potential difference between points A and B, VB−VA is defined to be the change in potential energy of a charge q moved from A to B, divided by the charge." at Physic Libretexts May 28, 2021 at 16:40
• but my text book used the opposite definition, maybe there's no convention yet May 28, 2021 at 16:41
• did you mean V12 the first time and V21 the second time? was it a typo (one big reason I am coming here, to know whether there is any typo in my tb) May 28, 2021 at 16:43
• (i) "'the electric potential difference between points A and B, VB−VA[,] is defined to be [...]'" Here, the sense of "the potential difference between A and B'' is made clear by the inclusion of $V_B-V_A$. The sentence would mean the same thing if "the potential difference between A and B'' were omitted. (ii) No, I meant that neither $V_{12}$ or $V_{21}$ has a meaning that can be taken for granted. I used $V_{21}$ as an example. May 28, 2021 at 17:59