The size and direction of magnetic induction and force

1. May 16, 2016

darkprior

1. The problem statement, all variables and given/known data
Hello, I have this problem:
Four long straight parallel wires are placed in vacuum according to the picture, the distance between each wire is a = 20 cm. Through each wire flows electric current I = 20 A in the specified direction. What is the size and direction of magnetic induction in the middle of this system? What is the size and direction of the force acting on one meter of the bottom left wire?

2. Relevant equations
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3. The attempt at a solution

I drew the line of forces following the Ampere's right hand law, and also the vectors of magnetic inducion of each wire:

now my answer is how do I compute the size of the resulting induction, and my second question is how do I find out the force acting on 1 meter of the lower left wire?

2. May 16, 2016

andrewkirk

Do they really want to know the strength of magnetic induction? Won't that be zero, because induction arises from the time variation of mag fields and this system is steady state? The vectors you have drawn are of mag fields $\vec B$, not of induction.

If it's just the mag field that's wanted, not induction, then the Biot-Savart law will do the job.

3. May 16, 2016

darkprior

Yes they want the strength of magnetic induction, if it is zero, then fine I will write it as a solution. Now can you please give me a hint with identifying the direction and strength of the force acting on one meter of left bottom wire, please?

4. May 16, 2016

andrewkirk

It is the Lorentz Force, which is explained here.

5. May 16, 2016

darkprior

Thank you for your help and time