Two infinitely long, straight wires are parallel and separated by a distance of

Question

Two infinitely long, straight wires are parallel and separated by a distance of 1.32 meters. They carry currents in the same direction. Wire 1 carries two times the current that wire 2 carries. On a line drawn perpendicular to both wires, locate the spot (relative to wire 1) where the net magnetic field is zero. Assume that wire 1 lies to the left of wire 2 and note that there are three regions to consider on this line: to the left of wire 1, between wire 1 and wire 2, and to the right of wire 2.


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Explanation / Answer

B = mu-nought I / (2 pi r). We'll put wire 1 on the x-axis and wire 2 at x = 0.99 B1 = mu-nought (5 I2) / (2 pi x) B2 = mu-nought ( I2 ) / [ 2 pi (x - 0.99) ] Here we are representing field vectors as positive if they go "into" the x-y plane, negative if they come "out" of the x-y plane. We could do it the other way; it makes no difference to this problem. We need B1 = - B2, so we set up: 5 / x = 1 / (0.99-x) 4.95 - 5x = x 4.95 = 6x x = 0.825 (meters) to the right of wire 1 In the region to the right of both wires, both fields point into the x-y plane; in the region to the left of both wires, both fields point out of the x-y plane.

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