Two long straight wires are parallel and are separated by a distance d . In the

Question

Two long straight wires are parallel and are separated by a distance d. In the diagram the wires are perpendicular to the paper. The left wire carries current i and the right wire carries current 2.7 i.

(a) Suppose the currents are in the same direction. In terms of i, d and constants, find the location, x, where the magnetic field is zero: x is measured from the left wire as shown.

(b) Suppose the currents are in opposite directions. In terms of i, d and constants, find the location, x, where the magnetic field is zero: x is measured from the left wire as shown.

Explanation / Answer

For an infinitely long straight wire, the magnetic field B = ( mo I / 2pr )

so

a)

uI/(2*pi*x) = u*2.7I/(2*pi*(d-x))

=> d-x = 2.7x

=> x = d/3.7 (between two wires)

b)

uI/(2*pi*x) = -u*2.7I/(2*pi*(d-x))

=> d-x = -2.7x

=> x = -d/1.7

so at d/1.7 toward left of both wire

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