Figure $1$: Illustration for problem $1.$

Figure $2$: Illustration for problem $2.$

$2.$ A thin "infinite" conducting strip of width $\backslash (2$ b$(-$b $\backslash$leq x $\backslash$leq b$)\backslash )$ is positioned in the $\backslash ($ x y $\backslash )-$plane as sketched in Fig. $2.$ It carries total current $\backslash ($ I $\backslash )$ in the positive $\backslash ($ y $\backslash )-$direction that is uniformly distributed across the strip. What is the direction of the resulting magnetic field $\backslash (\backslash$mathbf$\{$B$\}\backslash )$ at point $\backslash ($ P $\backslash )$ distance $\backslash ($ a $\backslash )$ above the central line of the strip. What is the magnitude $\backslash ($ B$($a$)\backslash )$ of that magnetic field as an exact function of distance $\backslash ($ a $\backslash )?$ How does the magnetic field $($approximately$)$ scale with distance $\backslash ($ a $\backslash )$ in the limiting cases of $($i$)$ very small: $\backslash ($ a $\backslash$ll b $\backslash ),$ and $($ii$)$ very large: $\backslash ($ a $\backslash$gg b $\backslash ),$ distances from the strip? Do these limiting behaviors make common sense as compared to other magnetic field sources we studied?