The trouble with that a point that is r from one wire is not going to be r from the other wire, unless the point is exactly half way between them. You pretty much need to express one of them as r and the other as .20 - r. This limits you to the plane of the two wires, but I think that is the unstated intent of the question. Anyway, you can now put in your known numbers and you'll have a nice equation with only the unknown r to solve for. Go for it!I set the two B equations equal to each other to solve for r, but am stuck on what to do once I set them equal to each other: B1=B2, muI1/2pir = muI2/2pir
A magnetic field between two wires is a region in space where the magnetic forces due to the two wires interact with each other. It is caused by the flow of electric current through the wires, and the strength and direction of the magnetic field depends on the distance between the wires and the amount of current flowing through them.
The strength of the magnetic field between two wires is calculated using the formula μ0I/2πr, where μ0 is the permeability of free space, I is the current flowing through the wires, and r is the distance between the wires. This formula is known as the Biot-Savart law.
The strength of the magnetic field between two wires is affected by the amount of current flowing through the wires, the distance between the wires, and the permeability of the medium surrounding the wires. The direction of the current and the shape of the wires can also have an impact on the strength of the magnetic field.
The direction of the magnetic field between two wires changes based on the direction of the electric current flowing through the wires. The magnetic field lines form circles around each wire, with the direction of the field being clockwise or counterclockwise depending on the direction of the current.
The magnetic field between two wires has various real-world applications, such as in electric motors, generators, and transformers. It is also used in particle accelerators, magnetic levitation trains, and magnetic resonance imaging (MRI) machines. Additionally, the Earth's magnetic field is a result of the interaction between the magnetic fields of its core and the outer core.