Can you describe and explain why segments along the x and y components cancel, f

Question

Can you describe and explain why segments along the x and y components cancel, for part a.

"A current I flows clockwise in a portion of
the annular loop shown. Find the magnitude and direction of the magnetic
field B at the point P, which is the center of the annulus. Briefly describe
which, if any portions of the current carrying conductors do not contribute to B, the magnetic field. "

and for part b,

"A current Iw flows in a long straight wire,
and current Il flows counterclockwise in the rectangular loop with its long side
parallel to the wire. Find the magnitude and direction of the net force on the
loop due to the wire. Briefly describe any forces that cancel, and indicate in
which directions these canceling forces point "

How do they cancel. Can you explain/show why. I've tried drawing and amperian loop and the right hand rule, but I'm not too sure.

I have the answers. I don't get the cancellation. I want to understand the syymetry here,

THanks.

Explanation / Answer

Hi, I

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