What is the magnitude of the magnetic field at the center of the arc?

[anna_628]

A current I = 3 A flows through a wire perpendicular to the paper and towards the reader at A and back in the opposite direction at C. Consider the wires below the plane at A and C to be semi-infinite. In the figure, L1 = 3 m, R = 6 m, and L2 = 6 m and there is a B = 2.37 T magnetic field into the paper (not including the field due to the current in the wire).

Caution: It may be necessary to take into account the contribution from the long straight wire which runs up to and down from the underneath side of the page.

Image: http://img28.imageshack.us/img28/5329/newpictureiv.png

What is the magnitude of the magnetic field at the center of the arc O due to the current in the wire (T)?

This is what I've done so far:
For the arc portion of the circle, I used B = Mu(0)xI/8R

For each of the straight portion, I used the equation for a long straight wire, which is: B = Mu(0) x I/(2 x pi x a).

Since each portion of the wire is going in a different direction (i, j, k components), I took each field, squared it and added them all then took the square root. But this is not the right answer...Not sure where I'm going wrong?

 

[Doc Al]

This is what I've done so far:
For the arc portion of the circle, I used B = Mu(0)xI/8R

This looks good.

For each of the straight portion, I used the equation for a long straight wire, which is: B = Mu(0) x I/(2 x pi x a).

What straight segments are you talking about? Note that none of them is infinitely long, which is what that formula is for. Discuss each straight segment separately.

 

[anna_628]

I guess I thought that this equation was for semi-finite straight wires as well...I don't know what the equation for it is if it is not this...

 

[Doc Al]

I guess I thought that this equation was for semi-finite straight wires as well...I don't know what the equation for it is if it is not this...

That equation is for a straight wire that is infinite in both directions. To find the formula for a semi-infinite wire, start with the Biot-Savart law. Hint: Look up how the formula is derived for an infinite wire and you'll see how to modify the derivation for a semi-infinite one.