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 4 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.

Explanation:

magnetic field due to a current carrying infinite wire

B = μ₀ / 4π x (2i / r )

i is current , r is perpendicular distance of point from the wire

Let at a point d distance away fro wire 1 , field is zero , let the current in wire 1 and 2 be 4i and i .

between them at any point  field will be in opposite direction .

magnetic field due to wire 1

B₁ = μ₀ / 4π x (2i / r )

= 10⁻⁷ x 2 x 4i / d

magnetic field due to wire 2

B₂ = μ₀ / 4π x (2i / r )

= 10⁻⁷ x 2 x i / ( 1 - d )

for zero field

B₁ =B₂

10⁻⁷ x 2 x 4i / d  = 10⁻⁷ x 2 x i / ( 1 - d )

4 / d = 1 /( 1 - d )

4 ( 1 - d ) = d

4 -4d = d

4 = 5d

d = 4 / 5

= .8 m