Please review my solution to the problem and explain in detail what I may be doing wrong and what concepts I may not be applying correctly.
The problem states:
A straight conductor carrying current i=5.0 A splits into identical semicircular arcs. What is the magnetic field at the center C of the resulting circular loop?
We know:
i=5.0 A
Using the right-hand rule, we know the magnetic field at the top of the arc is into the page and the magnetic field at the bottom of the arc is out of the page.
The magnetic field for the straight sections of wire produce no magnetic field at C.
Solution:
To determine the magnetic field acting on C, we sum up all of the fields.
B = Bin + Btop + Bbottom + Bout
B = 0 + -B + +B + 0
Magnetic field at C is negligible.