A long wire $($radius$,R=25\mathrm{.}0mm)$ with it's axis aligned with the $z-$axis carries a non$-$uniform current density. Assume the current travels in the $+$z direction $($out of the page$).$ The current density increases with the distance from the center of the wire. The current density in $(\frac{\text{A}\text{m}\text{p}\text{s}}{m^2})$ is given by: $J(r)=4r,$ where $r$ is the radial distance from the center of the wire, given in meters.

$(1)$ For point $p_1=15\mathrm{.}0mm$ on the $x-$axis $($inside the wire$)$:

$($a$)$ Find $I_{\text{e}\text{n}\text{c}\text{l}\text{o}\text{s}\text{e}\text{d}}$ : the current enclosed by the Amperian Loop of radius $15\mathrm{.}0$ mm centered on the z$-$axis. In this case, note that the current density is not constant so: $I_{\text{e}\text{n}\text{c}\text{l}\text{o}\text{s}\text{e}\text{d}}={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$jdA.

$($b$)$ Use Ampere's Law to find the magnetic field at point $p_1.$ Please provide your answer as a vector.

$(2)$ For point $p_2=50\mathrm{.}0mm($outside the wire$)$:

$($a$)$ Use Ampere's Law to find the magnetic field at point $p_2.$ Please provide your answer as a vector.

$($b$)$ Evaluate the line integral around the Amperian loop of radius $50\mathrm{.}0$ mm centered on the z$-$axis: $o{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$vec$(B)*vec(dl)$

$(3)$ For point $p_3=60\mathrm{.}0mm($outside the wire$)$:

$($a$)$ Use Ampere's Law to find the magnetic field at point $p_3.$ Please provide your answer as a vector.

$($b$)$ Evaluate the line integral around the Amperian loop of radius $60\mathrm{.}0$ mm centered on the z$-$axis: $o{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$vec$(B)*vec(dl)$