$2.[0/1$ Points$]$

SERPSE$1028\mathrm{.}4\mathrm{.}0$P$\mathrm{.}019.$

An arbitrarily curved wire that carries a current between two endpoints in the presence of a uniform magnetic field will experience the same net magnetic force as a straight wire carrying the same current between the same endpoints. Essentially, any forces experienced by parts of the wire that curve or twist away from the straight$-$line path are canceled out by forces on sections that curve back toward the original path. Furthermore, if the wire forms a closed loop in between the endpoints, the net force on the closed loop is zero.

Using this result, consider a town where the Earth's magnetic field has a magnitude of $\backslash (47\mathrm{.}8\backslash$mu $\backslash )$ T$.$ The magnetic field vector lies in a vertical plane defined by the north$-$south and up$-$down axes, and it points $\backslash (60\mathrm{.}0^\{\backslash$circ$\}\backslash )$ below the northward direction. In this town, a storefront window lies along the north$-$south vertical plane, and in the window is a neon sign $($which is a thin current$-$carrying discharge tube$).$ The sign carries a $35\mathrm{.}7$ mA current, starting from the lower south corner of the window, and ending at the opposite corner, which is $1\mathrm{.}47$ m to the north and $0\mathrm{.}850$ m upward. The sign spells out the word "DONUTS" between the two points. What is the net vector magnetic force $($in $\backslash (\backslash$mu $\backslash$mathrm$\{$N$\}\backslash ))$ on the neon sign? $($Take east to be the $\backslash (+$x $\backslash )-$axis, up to be the $\backslash (+$y $\backslash )-$axis, and south to be the $\backslash (+$z $\backslash )-$axis. Do not include units in your answer.$)$

$\backslash [$

$\backslash$overrightarrow$\{\backslash$mathbf$\{$F$\}\}\_\{$B$\}=$

$\backslash ]$