What would the magnetic field look like for a rod like this?

Imagine I have a long rod of metal. Let's say it's 1m long, 1cm wide and 1mm high. Now suppose I pass DC through it. But instead of running the current through lengthwise, I want to run it sidewise. That is, in ascii art:

                    \/ - attach "+" here
+-----------------------------------------+
|                The rod                  |
+-----------------------------------------+
/\ - attach "-" here


So, according to the right-hand rule, the magnetic field lines should encircle the rod length-wise. If I placed a small static magnet on top of it, it would theoretically start sliding towards one end of the rod (well, if it didn't flip over, that is). (This is what I'd like to achieve, in truth).

Somehow I don't think that would be the case. It seems more intuitive that the magnetic field should be the strongest in the middle, between the two points of attachment, and rapidly get weaker towards either end.

Is that so? I do not know where to start looking for formulas that would describe this, so I'm afraid I haven't done any prior research. Also - what could make the magnetic field equally strong at the entire length? If, instead of one point, I attached the electrical wire at 10 points on both sides, would that make it better? 100 points? How can I make that small static magnet slide from one end to the other when I flip the switch?

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This will probably give you some of the insight you are looking for as well as search terms <p> youtube.com/watch?v=1fRC7V3KMA4 <p> youtube.com/watch?v=MT4s-pxc9sM – neonzeon Dec 29 '14 at 23:00