$(0)$ A very iong and vertically$-$oriented, solid, cylindrical conductor carries a current I that is uniformly distributed in its cross$-$sectional area $($see Figure $1).$ The conductor radius is $20\mathrm{.}0$ mm and the current density inside the conductor is $95\mathrm{.}49kA{m}^{-2}.$

Figure $1.$ The vertically$-$oriented current$-$carrying conductor

$($i$)$ Completely state Ampere's Circuital Law and also express it mathematically.

$($ii$)$ State one $(1)$ drawback and one $(1)$ advantage of the law in $($b$)($i$).$

$($iii$)$ With the aid of Ampere's Circuital Law, determine vec$(B{)}_P,$ the magnetic flux density at the point $P(0,0,15)mm.$