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 11 and 12, which you need to find from a single measurement of the magnetic field B=Bx i + By j 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=0.96 cm, b=0.49 cm. A b 1 12 a a X Given the measurement of the magnetic field: By=-0.4 G and By=-0.2 G, what is the unknown current 11?: 11= A. What is the unknown current 12?: 12= A.

Answer 1

Let the Iis'I 2 are along 2 - axis? M Şəlъ — В. в рот 2ПТ t до" х = а2 +b2. b In Т2 Т - Jq--L2 (by phagvvр . B1 hi Bx= - Ba cosa B2 cosa - -z Вя (в+в2) Cosp -0 B2 8 - ha By since - Bzsimo 2) ву= (в. -#2) sin 18 дот, 27 В, — До 12 २४ - ФИІЅ COSQ= in triangle (t) К. Т. b а) + А.Т. 23 By – 2ТІ 2 Ho (I2 + I2 शा т.)(а нь") -17)( 1 ) Ь ми hg До शा (Т.

divide ean ☺ Bu By -b (I, +12) a (Ig- [] Doy -0.2 0.49 (Iit I2) 0.96 (III) 2 - I2+ I2 = 3.92 ( I 2-12) 2.9 2 I 2 = 4.92 11 I 1 Ž 0.6 I 2 putting in ean 9 5 0.96X10-2 By = -0.2 = 2x1077 (0.612-12) [60.963°70.us)] X 10-4 x 10-45 2x10-4 = 2x10-7 (04)12 X 102 x 0.826 10-4 I2 = 4x20 -7 X loox 0.826 Izz 4 X 0.826 II 2 ² 3.03 Amben Ang I 2 = 0.6 x 310 3 As IL: 1.828) Amber direction of both current is some Cover