Three long, straight electrical cables, running north and south, are tightly enclosed in an insulating sheath. One of the cables carries a 21.3 A current southward; the other two carry currents of 17.2 A and 10.8 A northward. Use Ampere’s law to calculate the magnitude of the magnetic field at a distance of 10.0 \rm m from the cables. Express your answer to two significant figures and include the appropriate units.

1.3 X 10⁻⁷ T or 0.13μT

Explanation:

The magnetic field from the currents directed northward will point in one direction, and the field from the southward directed current will point in the other, so they will subtract.

The net B field is found by

B = μ₀I/2πr + μ₀I/2πr - μ₀I/2πr

B = (4π X 10⁻⁷)(17.2)/(2π)(10) + (4π X 10⁻⁷)(10.8)/(2π)(10) - (4π X 10⁻⁷)(21.3)/(2π)(10)

B = 1.34 X 10⁻⁷ T

which, in two significant figures is 1.3 X 10⁻⁷ T or 0.13μT