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I was looking at an example problem the Organic Chemistry tutor did, where he is finding the magnitude and sign of the potential difference between two points at different levels of potential. The problem is below.

Example Problem

I do not understand how he got that Vab is 7V, and not -7V. I believe that Electric field should be parallel to, and in the same direction as, conventional current here. From electromagnetism, we know that if the path traversed (here it is A to B) and electric field are in the same direction, then our resultant deltaV value is negative. The formula for this is below.

E&M formula for potential difference

So why did he get a positive potential difference value here?

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  • $\begingroup$ the dot product doesn't take a summation symbol. There's nothing to sum over: it's a scalar. Or it needs an $i$: what is "i"? $\endgroup$
    – JEB
    Commented May 9, 2023 at 18:33
  • $\begingroup$ The summation symbol is there because we are breaking up the path into infinitely small components $\endgroup$
    – Woody Chelton
    Commented May 9, 2023 at 18:35

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$V_{AB}$ can mean $V_B - V_A$ or $V_A - V_B$. I believe the former usage is more common, but both are encountered and ideally the meaning should either be clear from the context or stated explicitly. In this case the latter definition is being used. There isn't a deeper reason why the potential difference in question is positive.

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  • $\begingroup$ so to be clear then, if we're going from A to B, then the deltaV, or voltage, should be negative here, right? $\endgroup$
    – Woody Chelton
    Commented May 9, 2023 at 18:54
  • $\begingroup$ Yes, the change in potential when you go from $A$ to $B$ is negative. $\endgroup$
    – Puk
    Commented May 9, 2023 at 18:57

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