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This question already has an answer here:

Why is there a negative sign in the relation $$V=-\int \vec E · \mathrm d\vec r$$ between the electric field and the electric potential?

Is this because of some derivation in vector calculus because I have not been taught that approach to this concept yet (as I am in high school)? Does this also represent the fact in the direction of increasing electric field the electric potential decreases? How should one interpret the negative sign and integral intuitively in more complex non linear cases?

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marked as duplicate by Qmechanic Aug 12 at 22:21

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It is the integral form of

$$\vec{E}=-\vec{\nabla} \varphi,$$

which says that the field points from high potential to low and not vice versa. Just as with other concepts of potential or potential energy (say, gravitational), electrostatic potential is defined so that (positively charged) objects tend to move “down the potential hill”, not up it. It is also defined so that electrostatic potential energy is additive with other forms of energy such as kinetic energy.

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