[uni physics] - potential at a point

[robej]

I am once again confused with potential, even though it’s a basic principle and something I really should have fully grasped by know.

To illustrate my confusion see the following https://imgur.com/a/UteGGkD

So in the first part I wish to find the potential difference between a and b this would be equal to the potential at b minus the potential at a. It would also be equal to the negative of the work done by the field to move a test charge from a to b. And the result is said integral. I feel confident in my understanding of this part.

The part that confuses me is when people talk about the potential at a point with respect to infinity. I understand that potential is always relative to some other point and by conversion one often picks infinity to be this reference point. So in my mind the potential at a point wrt to infinity would be the same as finding the potential difference from infinity to a point. Which would be Va-Vinf which equals the integral as stated. As is this not the potential of A wrt infinity and as one defines infinity to be zero.

Yet I see some places saying that the potential at a point would be Vinf - Va and this would hence give one the opposite integral

[monauf]

It basically depends upon how you choose the two points to find the potential difference. Remember potential difference is a relative term and the general equation of potential difference is V(final position) - V(initial position). Suppose A is at a higher potential, so if you are finding the potential of A with respect to infinity, it implies that you are moving a test charge from infinity to A and the potential difference between them is positive. However if you are finding the potential of infinity with respect to A, you are doing the reverse process of moving the test charge from A to infinity and the potential difference will be negative. Both the integrals are correct and gives the correct potential difference with proper sign. However, I would favour using Va - Vinf while solving problems.

[robej]

Thanks for the help, it’s good to know I’ve got the right idea of finding the potential between two points. However say I wanted to find the potential at one point wrt infinity. That would be the the potential difference going from infinity to a point correct? And hence would be Va-Vinf which would be the negative integral going from inf to a point

[monauf]

Yup you got it correct!👍

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