Question

Circular Current Loop Given: Radius = a , in the pz-plane (0 = 1/4) B = B. 2, pivot on p ī in the + ên direction (0 = 1/4) Find: Torque (T) exerted on the current loop Torque unit vector î in cylindrical coordinates Include derivation for: dĒ force differential vector moment arm vector dī torque differential vector torque vector

Answer 1

diFlotal = pdo 02, I Given A circular Content Coop having the facrorening dalia. Paciens ca It is in the pz.plane of angle ø= the (worent į in the positive B = Boês ô disection of an angle of (5 ) the magnetic field is C B = Boi with possot on p. the torque Excerted on the coorrent, Coop is given by .p. de wheere di is the torque differential vector its erabee is given by S dr = ex dif Here de = force differential vector. from the circular current loop, we can consider a snaes Element de having the acadis is a de = pdo the force exerted on the commend Coop is de = edi x8

B dF = IP do ân x B 22 Bed in the given dala the magnetic field is 3 = Boâconverting this into spherical coordinate system then sino o coso 1 rol Aol = coso o sinolol lo I o (B) ssino () +0(0) + cosole) COSO () +00) - Siro () 106) +1(0) 40(.) I coso eo7 -SinOB. wherre o is an angular distance of dl from Zai Ap = COSOB ; A = -@. Sino : B = COSOB â, - Sino a Subs lilait the above fan in de theo dF = IP do x [coco e, â, - sino bão] df - IPB.coso do âg

& ad dit 1 de Lef us coneideer o Similar Section of length di in crout opposite nosition of do. 1 from the dig, moment arm = ap moment arm sector a apag It is substitute in the differential Parque vector dre = px de = o pâ, x (-1,B.coso do ão) di . + 25 PB.coso doão Total targer , F lor = 5 ore Bocoso do ão = as fºl. coso do âo - 0888, (- siroja = or pB. I-san at sio o] Torgere, p=0