Question

Two parallel long (infinite for our purposes) wires are oriented along the z-axis. The figure below shows the (xy)-plane perpendicular to the wires, including the positions where the wires cross this plane. The wires carry some unknown electric currents I₁ and I₂, which you need to find from a single measurement of the magnetic field B=B_xi + B_yj at point A, whose position in the plane is also indicated. We will treat the currents algebraically: the current I is positive when it runs in the direction of the z-axis and negative when it runs in the opposite direction. In the right-hand system of coordinates, the z-axis is directed out of the screen towards us. The geometric parameters are known: a=0.62 cm, b=1.21 cm.

Given the measurement of the magnetic field: B_x=0.0800000000000001 G and B_y=0.72 G,

what is the unknown current I₁?:
I₁= ______ A.

What is the unknown current I₂?:
I₂= _____ A.

A b 1 I a a X

Answer 1

> Now field due to Iz 7 Magnetic field by I, at à B. - Mo I, 2stro 48x107 II arr b a r= √ a²+ b² = 1:36 cm => Bi 2x10 1.4 7x105.1, 1.36x10² Tano = b 1.21 0.62 62.86954 -5 B- - B, co B, cosoi + B. ht (=1047 - 5 I, T sino, COS62.87 +1-47 (0562.8j) xic -0.67197 +1.3074 ; x1 (-0-66441 +0:130741), (11= 104 6. 140-0 B₂ for cos (90-0) T + B sinfo oli) +0.0671aj) 2 G. con solving) -10.130 74 ;

BE = B, t B2 --006711,1 + 0.1307 Ij 201307 Izi -0.0671 F₂ j -(0.06715, +0.1307 1z) +601307 I, 20.064 iz) j Given B = Bail + Bys -0.081 + 0.72 3 >> 0.0671 I, 70-1307 -0.08 0:1307 I, -0.0672 0.72 solving we get I = 4.109 A Iz = -207217A I, = 4.11A I=-9.722 A