Two wires are aligned along the z-direction. Wire 1 is positioned at (x, y) = (0

Question

Two wires are aligned along the z-direction. Wire 1 is positioned at (x, y) = (0 mm, 0
mm) and carries a current of 0.5 A flowing in the positive z-direction, and Wire 2 is positioned at (x, y) = (5.4 mm, 0 mm) and carries a current of 0.4 A flowing in the negative z-direction. Find the magnitude and direction of the magnetic field at the location (x, y) = (7.2 mm, 0 mm). Hint: Apply Ampere’s law to each wire individually first, using appropriate separate loops. Recall that the magnetic field is a vector, so magnetic fields from different sources of current add as vectors

Explanation / Answer

The formula for the magnetic field around a current carrying wire is

B = oI/2r

From wire 1

B = (4 X 10-7)(.5)/(2)(7.2 X 10-3)

B = 1.39 X 10-5 T pointed directly upward (positive y)

From wire 2

B = (4 X 10-7)(.4)/(2)(1.8 X 10-3)

B = 4.44 X 10-5 T pointed directly downward (negative y)

Net field is 4.44 X 10-5 T - 1.39 X 10-5 T = 3.05 X 10-5 T pointed downward (negative y)

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