Portals and Electromagnetism
Of course, portals currently don't exist (unfortunately) which makes this all purely speculative. But let's assume for a second that they do, as they are portrayed in the games. As they are portrayed in the games, here are a few things that will be important for the upcoming situation:
1. Each open portal has one linked side and one unlinked side.
2. Everything going through a portal will have its mass and energy conserved.
3. Anything that reaches a portal's event horizon will pass through the portal.
With this in mind, let's look at figure 1 below. The U-shape is a magnet. Anything that is purple in the picture has a net negative charge, and anything that is red has a positive charge. The brown lines indicate the back, unlinked side of each portal.
The field that extends from the magnet passes through the wall and beyond the unlinked side of the portal, allowing it to reach the other side of the same portal. The positively-charged magnet is pulling the negatively-charged cube from behind the portal. Since the magnetic field is passing through the unlinked side of the portal, the field should not reach the exit of the other portal. As soon as the cube passes completely through the blue portal, it is no longer within range of the magnetic field and will stop being pulled, correct?
Figure 2 makes things slightly more complicated. Here, we have the negatively-charged magnet in front of the blue portal, pushing the cube into the portal. Due to a portal's conservation of energy, the field extending from the magnet should theoretically pass through the portal and continue out the orange portal. The moment the orange portal is fizzled, the blue portal has two unlinked sides, which will allow the field to pass through to the other side of the wall that the blue portal is on. The same applies if the blue portal is moved to a different surface.
So to those who are more familiar with forces such as electromagnetism, how do you think the field would behave alongside portals?
Actually, incorrect. I discussed this with a ex-physics teacher that works at my work, and he helped me draw this up (after much discussion on the inner theoretical workings of portals). Eg;
PortalStories.com
"Oh, in case you got covered in that repulsion gel, here's some advice the lab boys gave me: DO NOT get covered in the repulsion gel."
Interesting. If I'm reading that correctly, the magnetic field remains present on the other side of the portal in situation 1, but at one-fourth the intensity. And that probably alters situation 2 (with the magnet in front of the portal) a little bit as well. I'm guessing most of the field would pass through the portal, but a little bit (probably one-fourth again) would be present behind the wall on which the blue portal is placed. Hopefully I got at least part of that right. 
At any rate, thank you. I'm trying to use Hammer to make magnets that work through portals, and my initial diagrams were my best guess of how that would play out in real life.
Oh sorry, was concentrating on the first pick that I forgot about the second. Wouldn't the box have to be a negativley charged magnet for it to be pushed away? And the pushing power would work through the portals just as pulling power would.
A couple of things to keep in mind about my theory though;
1) The pulling power that is tranmitted through the orange portal will negate the conservation of momentum, and might cause the object to 'bob' back and forth between the magnets, depending on the initial force applied to the object and the strength of the magnet. This is caused by the magnet pulling the object into the portal, which in turn throws it out of the second portal, only to be pulled straight back in, causing the bobbing effect that is also seen with two horizontal portals under the influence of gravity.
2) The strength of magnetism is quartered at the distance squared. So if the strength is 1 at 1 meter, it will be .25 at 2 meters. Remembering that portals conserve everything and as such will have no effect of the strenght of magnetism.
PortalStories.com
"Oh, in case you got covered in that repulsion gel, here's some advice the lab boys gave me: DO NOT get covered in the repulsion gel."
I colored the box a lighter purple so it wouldn't overlap with the dots of the purple field in figure 2. So yes, it is negatively charged, and is thus pushed away from the negative field of the magnet.