Calculating Magnetic Field in Infinitely Long Wire: Step-by-Step Guide

[watsonds1]

In figure both currents in the infinitely long wire are 8A in the neg. x direction. The wires are separated by the distance 2a=6cm.
(b) what is the magnetic field at the origin
I found this to be zero
(c) Find the magnetic field at points along the z axis as a function of z.
I don't even know where to begin
(d) At what distance d along the positive z axis the the magnetic field a maximum?
(e) What is this maximum value?

I feel as though I have to find out (c) before I can do (d) or (e). If someone could help me get a start on this I would greatly appreciate it.

Relevant eqns.

[F][/B]/L=(mu*I1*I2)/(2*pi*a)
$$\oint$$ B $$\bullet$$ ds = mu*I
B=(mu*I)/(2*pi*a)

Please help me out. Thank you in advance

 

[Sethric]

(b)You are correct
(c)For this you can use:

$$B = \frac{\mu_0 I}{2 \pi r}$$

to find the magnitude of the magnetic field from each individual wire at a particular z value. In this case the r will be the hypotenuse of a triangle with base a and height z. Use some trig to calculate magnitude. Then think about what the right hand rule would say about the direction of the field vector (hint: it should be in the x and z directions only). That should give you a value for the magnetic field contribution from each wire for arbitrary z. After that, how would you normally find maximum values for a function of one variable? (for (d) and (e).)

Let us know if you need more help.