The electric potential can be defined as(adsbygoogle = window.adsbygoogle || []).push({});

V = - ∫_{C}E⋅dl

where we are taking the line integral along C from some convenient reference pointO, where we have set V = 0, to the pointrwe are trying to find the potential at. Of course, C can be any curve, but it's usually the most convenient to take it as a straight line fromOtor.

Doesn't this mean dlwill point in the direction fromOtor? If that is the case, then say we're trying to find the potential at some distance from point charge +q and we've set our reference point infinitely far away. We haveE= (kq/r^2)r(hat), wherer(hat) is the spherical unit vector. Then,E⋅dl= Er(hat)⋅dl. But dlpoints from infinity to the point we're trying to find, and say that we've pickedOso that dlpoints in the -r(hat) direction. Then,E⋅dl= -Edr, so evaluating the integral, we get V = -kq/r, which is evidently wrong.

I am aware that we can fix this by takingOto be somewhere else, but do you always take the line integral to be positive? If so, why? Or is there something else I'm missing?

EDIT: This seems like it'd fit better in General Physics. Woops.

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# I The sign of F (dot) dl when finding electric potential

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