Problem $2(3\mathrm{.}5$ P$)$:

a$)(0\mathrm{.}5$P$)$ Obtain the expression for the magnetic field for an infinite rectilinear conductor through which a current I flows, at a distance $\backslash ($ r $\backslash )$ from the conductor.

Two infinite and parallel rectilinear conductors through which the same current $\backslash ($ I$=3\backslash$mathrm$\{$~A$\}\backslash )$ flows in opposite directions are separated by a distance $\backslash (2$ a $\backslash )($see Figure$)$:

b$)(1$P$)$ Calculate the magnetic field at the midpoint, P $,$ between both conductors.

c$)(2$P$)$ Calculate the magnetic field at point $\backslash ($ Q $\backslash ).$

$[$Data: $\backslash ($ a$=10\backslash$mathrm$\{$~cm$\}$ ; y$=5\backslash$mathrm$\{$~cm$\}\backslash )]$