Wires L_1 and L_2 very long in length carry l_1=15A and I_2=-15 Amps, equal valu

Question

Wires L_1 and L_2 very long in length carry l_1=15A and I_2=-15 Amps, equal value, but each in opposite direction. They are also separated by 10 cm as shown in the figure below required to measure to measure the magnetic field B, in three places namely, at the center, at p_1 where x_1= 10 cm from L2 and at p2, where x_2 = 15 cm from L_1. What is the magnetic field and direction produced at the center, B_center, due to L_1 and L_2? What is the magnetic field and direction produced at p_1, B_p1 due to currents of L_1 and L_2?

Explanation / Answer

(a)
Magnetic Field due to Current carrying wire is given by,
B = (uo*I)/(2**r)

Bcenter = (uo*I1)/(2**r) + (uo*I2)/(2**r)
Bcenter = (2*10^-7*15)/(0.1/2) + (2*10^-7*15)/(0.1/2)
Bcenter = 12 * 10^-5 T
Direction = Into the Page.

(b)
Bp1 = - (uo*I1)/(2**r1) + (uo*I2)/(2**r2)
Bp1 = - (2*10^-7*15)/(0.1 + 0.1) + (2*10^-7*15)/(0.1)
Bp1 = 15 * 10^-6 T
Direction = Out of the Page.

(c)
Bp2 = - (uo*I1)/(2**r1) + (uo*I2)/(2**r2)
Bp2 = (2*10^-7*15)/(0.15) - (2*10^-7*15)/(0.1 + 0.15)
Bp2 = 8 * 10^-6 T
Direction = Out of the Page.

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