Why does the current across the cross section of an element, with perpendicular area vector ##d \vec{A}##, have a normal integral symbol in its definition:(adsbygoogle = window.adsbygoogle || []).push({});

##i = \int \vec{J} \cdot d \vec{A}##

Why is it not a closed surface integral?

##i = \oint \vec{J} \cdot d \vec{A}##

Usually we take the current density ##\vec{J}## to be parallel with ##d \vec{A}## (current density uniform) as to derive this equation:

##i = \int \vec{J} \cdot d \vec{A} = J \int \cos (0°) dA = J \int dA = JA##

##i = JA##

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# Curiosity about current density

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