15. The sketch shows four infinitely long parallel wires carrying equal currents

Question

15. The sketch shows four infinitely long parallel wires carrying equal currents of I 1.0 A that are flowing into or out of the plane of the sketch. The wires pierce the plane of the sketch at the corners of a square, each side of which is L = 0.200 m long. Current flows into the sketch at A and B, and flows out of the sketch at Cand D. Find the magnitude and direction of the net magnetic field at point P - the center of the square. AXC A) 0T B) 4.0 x 106T. down C) 1.0 x 106 T. up D) 1.0 x 105 T. down E) 4.0 x 10 T. up BXD

Explanation / Answer

magnetic field due to current in wire , B = Uo*i/(2*pi*d) = 4*pi*10^-7*1.0/(2*pi*0.141) = 14.184*10^-7 T

where d = L/2^0.5

magnetic field due to wires C , D

is Bnet = (2^0.5)*B = 1.414*14.184*10^-7 = 20.05*10^-7 T

magnetic field due to wires A , B is same as due to C , D

so net field at P is = 2*Bnet = 40.1*10^-7 T it is in downward direction .

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