This is taken from Introduction to Physics (8 edition) Chapter 21, Problem 63 Tw

Question

This is taken from Introduction to Physics (8 edition) Chapter 21, Problem 63

Two infinitely long, straight wires are parallel and separated by a distance of one meter. They carry currents in the same direction. Wire 1 carries 6 times the current as wire 2 does. Determine the perpendicular distance from wire 1 to a point where the net magnetic field is zero between the two wires.

Please kindly assist.

This is taken from Introduction to Physics (8 edition) Chapter 21, Problem 63 Two infinitely long, straight wires are parallel and separated by a distance of one meter. They carry currents in the same direction. Wire 1 carries 6 times the current as wire 2 does. Determine the perpendicular distance from wire 1 to a point where the net magnetic field is zero between the two wires. Please kindly assist.

Explanation / Answer

Let current through the first wire is i1 then the current through the second wire is i2=6i1 the istance between the two wires is s let d isthe distance of the point from first wire where the magnetic field is zero then it is at a distance s-d from the second wire using Amperes law the magnetic field due to firstwire is B1=i1/2d magneticfield due to second wire is B2=6i1/2(s-d) the net field is zero so B=B1-B2=0                                          i1/2d-6i1/2(s-d)=0                                           1/d-6/s-d=0                                           d=s-d/6                                          7d=s                                            d=s/7

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