Force between Parallel Wires: Calculating Resultant Force

[rohanlol7]

1. The problem statement, all variables and given/known
Two long parallel vertical wires 0.3m apart are. ' placed east-west of one another. The current in the westerly wire is 30A and on the other 20A. The horizontal component of the Earth's magnetic flux density is 2*10^-5. Find the force per unit length on each wire. (The answers are 0 and 1mN but I don't know why)
I calculated the force on each wire due to the earth. Then I calculated the force due to the wires. Thesr 2 forces are perpendicular so I used pythagoras to find resultant but my answer was wrong

Homework Equations

The Attempt at a Solution

 

[nuclear_chris]

May I suggest you first figure the magnetic field (or magnetic flux density) on each wire due to the other wire. The magnetic field can be obtained using Amps Law. From the magnetic field you can then obtain the magnetic force which in this case is given by F=I*L*B where I is current, L is the length of the wire and B is the magnetic field. You only need the Force per unit length or (F/L)=I*B, so all you really need to do is compute the magnetic fields on the wires and you should be good to go. Don't forget to add the magnetic force on both wires due to the Earth.