# Magnetic Field of Two Wires

1. Mar 9, 2008

### ttiger2k7

[SOLVED] Magnetic Field of Two Wires

1. The problem statement, all variables and given/known data

If r = 30.0 mm, i = 2.00 A, and i' = 8.60 A, what is the magnitude of the magnetic field at the center point?

2. Relevant equations

B=($$\mu$$$$_{0}$$I)/(2pi*r)

3. The attempt at a solution

I applied biot-savart's law to i and i', and added them together.

For B_i:

(4pi*10^-7*2)/(2pi*.03) = 1.34*10^-5

For B_i':
(4pi*10^-7*8.6)/(2pi*.03) = 5.74*10^-5

B_center = B_i + B_i' = 7.08*10^-5

Which is not correct. I'm pretty much sure my method at solving the problem is completely wrong. I just don't know what exactly is the right steps to take. Any help would be appreciated.

2. Mar 10, 2008

### jlg

biot-savart for a loop is u*2*pi*I/4*pi*R, which simplifies to u*I/2*R.. you're only looking for half a loop so 1/2 * that is equal to u*I/4*R ..

The total mag field would thus be: u*I'/4*R + u*I/4*R

u = 4*pi*10^-7, by the way.

Last edited: Mar 10, 2008
3. Mar 10, 2008

### ttiger2k7

Ah, thanks! Got it.