# Homework Help: What is the magnitude of the magnetic field at the center of the arc?

1. Apr 14, 2010

### 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 [Broken]

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?

Last edited by a moderator: May 4, 2017
2. Apr 14, 2010

### Staff: Mentor

This looks good.
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.

3. Apr 14, 2010

### 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...

4. Apr 15, 2010

### Staff: Mentor

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.