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\f4. ) 10 -s unit vector pointing from wire # I to the Olorigin) 520 TIO 62 )x Flo = Tio IFial ( - a , - b ) = ( a , b 120 = ( or-b ) = (9 , -? ) RMR 3 = 2 2 2 x- y = + RHe D the origin ... f =-y - SX 5.) Biot - Savert Law dB = Moi ds x F 4 7r 2 d's = ds ( divection of wire or current ) ds = ds ? = direction of current , coming out of the board dB = Moi ds(3 x r) direction magnitude bi = SIX rio = Exlax by bi = - a y + b x = (b, _) = a2 +62 =bi = ( 2 , 2 ) Ex( - 9 2 - 46] 120 = ( 9 : 7 ) bi = ( b , 7 ) 62 = (b , 9 ) sol'n : 'b2 = Ex( a x - by ) b2 = ( qutb x ) " ) magnetic field : magnitude a direction B1 = Moll bl = Moil 20r 2 xr ( b , a B = B, + B2 = MO bib tizb 2ar _ T. r 32 = Moiz by = Molz ( b , 2 1r a 2 1r - ail + 9iz = Mo Libtizb, iza - iza] 2 Tr 2 B = MO [ (itiz ) b, (62 -il) a, o ] - 1 2 1/ 2 8-) Force ca'n : F = qV x B = q ( v+ , vg, v2 ) x Mo [ (vitz)a, (12-vi)a, 0] 2 1r 2Two infinite wires carry current in the Z direction have position vectors in the xy-plane of #; = (a, b) and 7, = (a, b) with corresponding currents i;and i,, respectively. Analyze and solve the following problems in the xy-plane (i.e. z = 0): 1) 2) 3) 4) 5) 6) 7) 8) Draw a picture representing the above scenario including a co-ordinate system and the angles between the position vectors of the wires and the x-axis Determine a value for the cosine and sine of the angles in part 1) in terms of the given co- ordinates Determine the distance of the wires from the origin in terms of the given coordinates Determine the unit vectors pointing from the 2 wires to the origin (label them #; and #4,) in terms of the cosine and sine found in part 2 Determine the unit vector of the magnetic field at the origin from both wires (call them b; and b,) Determine the magnetic field at the origin from both wires (call them B, and B,), and draw these vectors on the diagram from part 1) Determine the total magnetic field at the origin, B For a particle with charge g and velocity vector # = (vx, vy,vz) determine the force on the particle at the origin