Scenario$-1$: Three long, parallel $($real$)$ straight wires pass through the vertices of an equilateral triangle with sides

equal to $10cm.$ Each wire carries $15A.$

Scenario$-2$: A straight wire carries a current of $20\mathrm{.}0A.$ A rectangular coil with two sides parallel to the straight

wire has sides that are $5\mathrm{.}00cm$ long and $10\mathrm{.}00cm$ long. The side nearest to the wire is $2\mathrm{.}00cm$ from the wire. The

coil carries a current of $5\mathrm{.}0A.$

NOTE: Questions $($a$),($b$)$ follow Scenario #$1,$ and $($c$),($d$)$ follow Scenario #$2.$

$($a$)$ In what direction will a proton deflect if it is shot into the page, center to the triangle wire system?

$($b$)$ Find $($i$)$ the vec$(B)-$field intensity at the location of the upper wire due to the currents in the two lower wires by

drawing an accurate vector diagram. No math, and $($ii$)$ the force per unit length on the upper wire.

$($c$)$ Find the force on each segment of the rectangular coil due to the current in the long, straight wire.

$($d$)$ What is the net force on the coil? $[$Hint: vec$(B)-$field intensity weakens as you move apart from the source.$]$