The net magnetic field at the center

[PhysicsTest]

Homework Statement

Four, long, parallel power lines each carry 100-A currents. A cross-sectional diagram of these lines is a square, 20.0 cm on each side. For each of the three cases shown in , calculate the magnetic field at the center of the square.

Relevant Equations

$B = \frac {\mu_0 I} {2a}$

The current direction is as follows

I think so much and do the right hand rule i get 0 at the center, but not sure why the answer is non zero. I have shown the directions of the magnetic fields, i have not shown the magnitudes of equal length but they all are equal. Why the answer is non zero, what mistake i am doing?

 

[BvU]

I see only one case ? Mixup of answers ?

 

[PhysicsTest]

I see only one case ? Mixup of answers ?

The first two I could solve, this is the 3rd one which I am struggling to get answer.

 

[Gordianus]

May I suggest drawing the arrows again?

 

[PhysicsTest]

May I suggest drawing the arrows again?

I end up getting below the same,

 

[Gordianus]

No, try again.

 

[PhysicsTest]

No, try again.

Ok, chances are there of a below diagram

But a very tough one to know where it will be left. Am i correct here?

 

[Gordianus]

Try drawing the B-lines of each wire

 

[PhysicsTest]

Try drawing the B-lines of each wire

The B lines are like this

Everything seems to be left.

 

[Gordianus]

Good! Now extend the lines to the center and draw the arrows again.

 

[PhysicsTest]

Surely the tougher than i expected. Hope it is correct.

 

[Gordianus]

Victory!

 

[PhysicsTest]

Thank you very much for support.