Question

Please solve and explain how its done.

The figure below displays a thin conducting loop shaped as an equilateral triangle with the edge length L=7.05 cm. It carries current I=13.5 A. 1 P L L What is the magnitude Bo of the magnetic field produced by this current loop at point o in the center of the triangle?: G. Bo= What is the magnitude Bp of the magnetic field produced by this current loop at point P outside the triangle as shown in the figure?: Bp= G.

Answer 1

C 60 O Y B А Ha is dus to the sum of elements Magnetic field at point o due to OE Y OE a3 fied to AB is AC is abo aut of the page One side wire is AB, BC and Ac. Prependicular diskou to each side of the trinogle from the castre o is given by tan 30 adtaunt = 4 adjacent = AE to 30 = 2 x to the magnetic out of the page at o, due to be also out of the page and due to so, the majoetic field at point is three times field due to Magoch e field due to long straight B= Moi (sio id + sin(a) B MAI (aus 10.+cos (0.)) x = B = 68, 0 i = 02 = 30 B 4^(- (2 213 HOI XP B 2√3x Axx10 x 135x13 4XXXL ARX 7.05x10? B = 2x3x135 x 105 T = 11.49x105T Coat of the page? B 4 or 4r Ho I 7.05

So total B due to 3 sides is В = 3x || +1х10 °у -6 0 - 34.4+1х0 °

7 is the tr to side Bc A Bop is right angled tringle Bid 60 = 1 >r = Bpainsi BP=L BP 60260 B Vbo L Р Va Pc is the prependawar to side AC 30 60 AP AP=24 Pe=r2 = Apsinto - BAL is zero. the The point is along the side AB so due to point AB magnetic field at P So, the magnetic field at part is due to lengths Bed Ac. B Due to AC at point p is out of the the magnetic field is into the page. field the magnetic and due to Вс Boot В, + B Ас Вс out of page +ve (tz) into the page -ve (-2) Straight conductor (wow har Y Magnetic field due to a (cos + coses is the prependicular diskoue bekween core and pool 0.80, are the angles that sides made with the pool Ho I (cos (98) + cos 6o) (+2) hai (cos(3 033) B (+15) MOI BAC 'P 4 arz BBC An Moi - + 2 QV8 26 VEL VL A.KL

B HOI 4 TL 3-23 213 MI 8th B = MOR (213) (-2) > into the page B = 42x107x13.5 8xx 7.05X102 (2-15) 2 105x 13.5 14 (2-13) 0.258x105 T Cinto the page) am againing drawing the triangle I bere to make it clear. more L LOTI L DED A 7 LABC = <p80 (opposile angles are = 60 equal LeBP = 1200 (lisear pair) A CBp is issoceles triangles (BC = Bp=2) > <BCP - <BPC = 38. LA CB= 60 (equilakssal triangle) Lcp- qo. So, Pc is trto AC.