I worked through a problem and arrived at the final solution (which is correct), however, one part of it should equal zero mathematically. This is the part that should equal zero:
$F_{2i}= (\frac{μ_0I_1I_2}{4 \pi})$ $\oint_{L_1} \oint_{L_2} dl_{1i}$ $dl_{2j}$ $ (\frac{l_{2j} l_{1j}}{|\vec l_{1}- \vec l_2|^3})$
Is there any Kronecker-delta identity that would perhaps result in $dl_{1i}$ $dl_{2j}$ $=0$ ?
The line integrals are performed around closed loops L1 and L2, $\vec l_{1}$ represents the vector from origin to a certain point on L1, $\vec dl_{1}$ represents the difference in position from $\vec l_{1}$ and "another vector from origin to another point on that same loop". Same for loop L2 with $\vec l_{2}$ and $\vec dl_{2}$.
Ps. I also know that the exact same integral but with $dl_{1j}$ $dl_{2j}$ instead of $dl_{1i}$ $dl_{2j}$ is not equal to zero.