In several articles and books, I have read that "the magnetic force on or due to a small element of a circuit is equivalent to two or more of its component elements, provided that the current remains same".
i.e. the magnetic force on or due to AB(in red) is the same as the magnetic force on or due to its component current elements (in black)
However this doesn't make sense to me because in a closed circuit, the vector addition of current elements is zero. It means the resultant current element of a closed circuit is zero. Hence the force on or due to a closed circuit is zero. However this is not the case (a closed circuit experiences and exerts magnetic force).
Then how can "law of vector addition of current elements" be valid?