Simple EM Problem (not to me for some reason)

[FrogPad]

I'm unsure what I'm doing wrong here... it has to be something. So let me explain the problem:

I'm supposed to rank the net magnetfic field strength for various arrangements. In all of the arrangements the magnitude of the current is the same. The distance between each of the charges is the same. We are supposed to find the magnetic field in the center of each arrangement. (The center of the square)

The first arrangement looks like this (please excuse the ascii art)

  [*]------[*]
   |           |
   |           |
   |           |
  [*]------[*]

(EDIT: I've been trying to make this thing look pretty. I give up on it. It is just supposed to be a square)
This is supposed to be a cross sectional area of four wires that are run in parallel. The distance between each wire is the same. [*] means the direction of the current is running into the page.

Ok, so this is how I "thought" I should solve this problem.

We can use $$B = \frac{\mu_0 I}{2 \pi r}$$ to model the field strength at a distance $r$ from each wire. If we let [*] be a positive direction. Next, we use vector superposition to get the net magnetic field.

Thus:
$$B_{net}=B_1+B_2+B_3+B_4 = \frac{\mu_0}{2 \pi r} \sum_{n=1}^{4} I_n$$

We can drop the terms that are not changing because it's not relevant for the ranking. Thus:
$$B_{net} = I_1+I_2+I_3+I_4$$

So for the ASCII diagram I have, then:
$$B_{net} = 4I$$

However, the example we were given states that $B_{net} = 0$.

How am I not modeling this correctly. I guess I'm having a hard time visualizing how the circular magnetic fields are interacting with each other.

 

[Tide]

HINT: The magnetic field at a point is a vector - use the right hand rule to determine its direction.

 

[FrogPad]

That was an amazingly fast reply tide.

So would I think about the magnetic field at each point as a piece of the $\vec B$ with length $d\vec l$. Which I could just extend the length with a factor to think about it as a larger magnetic line.


So then using the right hand rule I would have four vectors.

Where the top two oppose each other, and the bottom two oppose each other. Which cancel to get 0?

So am I just making a mistake on the sign I'm choosing for $I$

 

[Tide]

You're doing fine! Here's a pointer or two:

If a wire is straight then the magnetic field it produces will be azimuthal. That will be true no matter how long they are. In your case, all you have to do is recognize they each produce the same (magnitude) of magnetic field and all you have to concern yourself with is their direction.

And, there was nothing special about the speed of the reply - I just happened to be here just after you wrote.

 

[FrogPad]

Cool. Thank you.

By the way. I didn't mean to imply that anything was special about the speed of the reply. It was just surprising. I was trying to fix that stupid ASCII drawing of the diagram, and I kept clicking on save. Then all of a sudden there was a reply here. I've just never had that happen before.

Anyways... thanks for the help. I appreciate it.