The distance where the magnetic field of two wires is zero

[DottZakapa]

Homework Statement

The distance between two parallel long wires, carrying currents equal to i and 3i respectively, is d as shown in the picture. What is the distance from the wire carrying the current i at which the magnetic field is zero

Relevant Equations

guess biot-savarat

Homework Statement: The distance between two parallel long wires, carrying currents equal to i and 3i respectively, is d as shown in the picture. What is the distance from the wire carrying the current i at which the magnetic field is zero
Homework Equations: guess biot-savarat

Being two long straight wires i can apply Biot-Savart equation. The currents are flowing in the same direction, hence at some point in between the sum of the two magnetic fields cancels.
My attempt
μ₀i/(2πd)=μ₀3i/(2πd₁)
and solve for d.
But does not leads to the correct solution. can't spot the mistake.

 

[Delta2]

There is some confusion in your post regarding the use of symbol d. It is used to indicate the unknown distance and also the known distance d between the two wires.

Lets call x the distance from wire carrying current i of point P where the magnetic field is zero . Then the distance of point P from the other wire is d-x. What equation can you make using those distances?

 

[DottZakapa]

don't know why i couldn't find a way to express it...now i got it.
i/x=3i/(d-x) ... ⇒ x=d/4
Thank you, very kind