Magnetic field at origin because of 3 wires

[irishbob]

Homework Statement

Determine the magnetic field (in terms of I, a, and d) at the origin due to the current loop shown in Figure P30.14. (Use mu_0 for µ0, pi for π, a, d, and I as necessary.)

http://www.webassign.net/pse/pse6_p30-14.gif

Homework Equations

B=mu_0(I)/(2pi*r) for straight lines

The Attempt at a Solution

http://www.webassign.net/cgi-bin/symimage.cgi?expr=2%28%28mu_0%29I%29%2F%282pi%2Asqrt%28d^2%2Ba^2%29%29-%28mu_0%29I%2F%282pi%2Ad%29&size=4

What I did was, since the ones on the left and right are equal, and in the same direction, I found the distance between the two wires (the square root in the equation), plugged that in for r, and multiplied it by 2. For the horizontal wire, I just plugged d into r. This is in the opposite direction by right hand rule, so I made it negative.

What am I doing wrong? Help!

 

[Redbelly98]

Homework Equations

B=mu_0(I)/(2pi*r) for straight lines

That equation only works when the wires can be considered infinitely long. That is not the case here.

Do you have any other formulas that deal the magnetic field due to a wire of any length?

 

[irishbob]

Ah.

Well there's the B-S law
B=(μ_0*I)/(4pi)*∫(d*(l x r(hat))/r^2

and

Ampere's law:
∫(enclosed) B·dl=μ_0 I(enclosed)

and for Ampere's it has to be highly symmetrical with constant field for us to use it easily.

I still don't know which to use. It seems like it would be difficult to use Ampere's law because the field isn't uniform. Or is it? I'm not so great at this :P

 

[Redbelly98]

The Biot-Savart law is the one to use.

 

[irishbob]

Thanks! :D