validity of “law of vector addition of current elements”

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?

• If you have a closed circuit then the net force can be zero. Think of a rectangular coil in a motor where the not force on the coil is zero but there is a couple acting on the coil. – Farcher Oct 14 '16 at 13:06
• @Farcher: The net force can or cannot be zero generally. But according to the question it would necessarily be zero. – N.G.Tyson Oct 14 '16 at 13:11