A Circular Metal Loop of Radius 10 Cm and Three $I _ { 1 } = 60 \mathrm {~A} ,$

Multiple Choice

A circular metal loop of radius 10 cm and three long straight wires carry currents of $I _ { 1 } = 60 \mathrm {~A} ,$ $\mathrm { I } _ { 2 } = 20 \mathrm {~A} ,$ $I _ { 3 } = 70 \mathrm {~A} ,$ and $I _ { 4 } = 30 \mathrm {~A} ,$ as shown in the figure. Each of the straight wires is 20 cm from the center of the loop. The axes are shown in the figure, with the +z-axis coming out of the paper. What is the z component of the resultant magnetic field at the center of the loop? (?₀ = 4? × 10^-7 T ? m/A)

A) -360 ?T
B) +360 ?T
C) -40 ?T
D) +40 ?T
E) -170 ?T