Given the current density, →j, one can always determine the current through a surface with area, A, and normal vector, ˆn: \[I=A(→j⋅ˆn)\...Given the current density, →j, one can always determine the current through a surface with area, A, and normal vector, ˆn: I=A(→j⋅ˆn) If the current density changes over the surface, one must take an integral instead: I=∫→j⋅d→A where d→A, is a surface element with area, A, and direction given by the normal to the surface at that point.
