Question

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 thecurrent 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.

Answer 1

Let point p lies between the wires at which net magnetic field is zero

magnetic field at a point P which is at a distance r from the first wire B_1 = μ_0 I / 2πr

magnetic field at a point P due to second wire which is at a distance 1-r from the second wire

B_2 =μ_0*6 I / 2π(1 -r)

From the given condition

B_1 = B_2

μ_0 I / 2πr =μ_0*6 I / 2π(1 -r)

solving for r we get

r = 1/7 m = 0.142 m