Magnetic field due to a current-carrying conductor:

$\overline{){\mathbf{B}}{\mathbf{=}}\frac{{\mathbf{\mu}}_{\mathbf{0}}\mathbf{I}}{\mathbf{2}\mathbf{\pi}\mathbf{r}}}$

Resolving vector components,

$\overline{)\begin{array}{rcl}{\mathbf{B}}_{\mathbf{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{B}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathbf{\theta}\\ {\mathbf{B}}_{\mathbf{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{B}}\mathbf{\right|}\mathbf{}\mathbf{sin}\mathbf{}\mathbf{\theta}\end{array}}$

**(a)**

$\begin{array}{rcl}\mathbf{r}& \mathbf{=}& \sqrt{{\mathbf{\left(}\mathbf{2}\mathbf{d}\mathbf{\right)}}^{\mathbf{2}}\mathbf{+}{\mathbf{d}}^{\mathbf{2}}}\\ & \mathbf{=}& \mathbf{d}\sqrt{\mathbf{5}}\end{array}$

${\mathit{B}}_{\mathbf{1}\mathbf{m}}\mathbf{=}\frac{{\mathbf{\mu}}_{\mathbf{0}}\mathbf{I}}{\mathbf{2}\mathbf{\pi}\mathbf{d}\sqrt{\mathbf{5}}}$

**Part A:** Point M is located a distance from the midpoint between the two wires. Find the magnitude of the magnetic field created at point M by wire 1.

Express your answer in terms of , , and appropriate constants.

**Part B: **

Find the magnitude of the *net* magnetic field created at point M by both wires.

Express your answer in terms of , , and appropriate constants.