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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?