Question

Find the magnitude (in N/m) and direction (in degrees counterclockwise from the +x-axis) of the force that each wire experiences in the figure by using vector addition. (Assume that the +x-axis is to the right and the +y- axis is up along the page.) 7.00 A 1211.0 cm 17 11.0 cm- х 14.0 AT 11.0 cm 49.0 A Top wire magnitude N/m direction o counterclockwise from the +x-axis Bottom left wire magnitude N/m o counterclockwise from the +x-axis direction Bottom right wire magnitude N/m º counterclockwise from the +x-axis direction

Answer 1

Sot - let → - the wires be denoted by A, B and a 7 A 7.00A K dd 11.00cm 11.00cm I = 7.00 IB = 14.04 I = 49.00 14.0A DE ug.oA 11.ooc 1 Top wire :- magnetic field at wire a due to B & c. here Pretoria e T +43) -7 10 X 49 11810-2 20127 x 10-5 (15ê +) Tesla 2 227

424 107 x 14 11X102 MIA (92 - 43) 107 X14 (- 43) 0.636 x 105 (13ê -3) B = Testa so Bnet - [9.636 x ($i - ;)] + [2-227715 (53 +9)] Bonet = 2.863 x 155 x ê + 1.591 X10S A Buet = (2.86313 i + 1.59 %) x10 s | Tesla force on wire A net - (R) x (2.86353 ê +1:59 19 ) x 105 = [34-712 (Ř xê) + 11.137 (K x 3 )] x 165 E = [34.712 j - 11:137 â] x265) Nam I so magnitude = 1134712) +(11:13752x10-5 = 36.454 X10N/m

direction o = tann 134-712 x 10-5. ( - 11:137X165 0 = 287-789° I counterclockwise from x -axis Be a • ii) Bottom left wire :- magnetic field at wire B due to A&C here and 2457X7 ( 943) - 0.315x70% (13 i -1) and Be - 18e (3) X10 Tesla und 11X10-2 O Toe - 4.454 X105 ] Tesla so Pet - B + BE = [0.318 4105 (532-5)] + [4.454 X10 5 f] Bomet = 0.550x10s i +4.136 X165 Tesla

Force on wire B - = [14 (-Å) x (0.550 ê +4.136 3 )] 155 7:7(+R) xtê)] x10+5 + 57.904 X16%[4-18) X (f] 17.7 -) + 57.904 2] x/59) Mm mag nitude x10 x 10 EI - J (7.0)2 + (57.904) 2 E = 58.413 x 169 Non direction 0 = tant / -7.7x105 (57.904x105, 10 = 352-42607 counterclockwise from X - axes (ii) Bottom right wire : - magnetic e due to field at wire A and B 0 30 here P - Bota ( +43) yad

E z (1 +43) 0.318 x 10-5 (Bê + 3) Tesla 47d ano To B - MIC (-5) - 70-7 x 19 (-) - 1.272 x 105 (-3) 11x 10-2 - Tesla • - = [0.318 x105 (Bê + ;)] + [1.272 4155 (-1)] Bret - [ 0. 550x105 ê - 0.954 Î x 105 ] Tesla Force on wire a = (49 (-R)] x [ 0.550 x16se - 0.954X10S }] - 96.95716 579) – 46.746x105i Nilai • magnitude - x105 El 1636.9552+ (46-746) - 107.631x1019? Non lerection o = tant (- 96.95x105. (-46.7468105 64.2580 counter clock bise from x-axis o =

This we found that i) Top wire magnitude = 36.4548105 N/m direction o = 287.7890 '") Bottom left wire magnitude - 58.413 X10 N/m direction o= 352-4260 iii) Bottom right wire magnitude = 107.631 8105 N/m direction o = 64.2580