 Problem Statement
 Calculate the net magnetic force on I2 due to I1
 Relevant Equations

Fmag = I * ([a] x [B1])
where:
[a] is a vector representing the length and direction of the wire carrying I2.
[B1] is the magnetic field vector due to I1 (Please see figure.)
I just need to confirm my intuition that the magnetic force on the wire carrying I2 is 0.
Basis for my intuition:
* Right above the center of the loop carrying I1, the magnetic field lines are in exactly the same direction as the piece of wire carrying I2, so [a] x [B1] = 0.
* I2's own magnetic field is curling around it (BiotSavart law and Ampere's law), and never goes through it, meaning an external field that actually goes through the wire will have no effect on it.
Note: only the shown section of the wire carrying current I2 is to be considered in calculations.
Is my intuition correct?
Thank you