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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:
Why is it not a closed surface integral?
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##
##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##