Magnetic Field at the Center of a Coil

[Dart82]

Homework Statement

The radius of a single coil of wire is 0.22m. It carries a 200 A current that flows clockwise.
A long, straight wire carrying a current of 310 A toward the right is located 0.05m from the edge of the coil. What is the value of the magnetic field at the center of the coil? Answer should be in gauss. (1Tesla = 10,000 gauss)

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Homework Equations

Magnetic field at the center of a flat circular coil: B = (4pi*10^-7)I / 2R
Magnetic field created by a long strait wire: B = (4pi*10^-7)I / 2*pi*r

The Attempt at a Solution

The way i think about this problem is this: I know the wire will create its own magnetic field, this field will extend into the field created by the coil, thus increasing the total magnetic field. I solved for B created by the long straight wire, then solved for the B created by the flat circular coil. Next, i added the two magnetic fields together and converted T's to g's.

 

[rootX]

But doesn't conductors shield their interiors?
So, that means the outer straight wire has no effect @ the center of the coiled wire?

 

[Dart82]

I'm not sure, but i know if i only calculate the field for the loop i get 5.7 gauss which is not the correct answer.

 

[Weimin]

I think you are right, just add two of them because they are parallel.