Horizontal magnetic attraction? I came across and interesting effect today, I have a dozen of Neodymium magnets around my house. And, they are very strong. Anyhow, one of them got attracted to my large steel plate table(use for cutting and building). It was almost impossible to take it apart, till I contacted the manufactured of those magnets and they proposed to slid it off. Amazingly, it worked. But what shocked me is the level of huge force decrease. It's like I'm going against friction alone... Only at the edge of the plate I felt a force that is strong, but half way through... The magnet as almost "off" only the edge of the magnet was attracted strongly to the edge of the plate, what explains this?
 A: the magnetic force is downwards towards the plate. friction is a fraction of this downward force (look up coefficient of friction) and is antiparallel to the sliding force. therefore sliding a magnet across steel always requires less force than lifting it (as long as the coefficient is less than 1--usually the case with metal on metal). 
once you reach the edge of the plate the direction of the magnetic force rapidlt changes more and more as the plate moves away and to the side. now the magnetic force pulls almost sideways instead of only downwards, and in the opposite direction of the sliding force. this only occurs for a moment, but is significant enough to detect as a large impulse. 
A: The field of the magnet is evenly distributed upon the metal plate thus making the magnet seem to be at a neutral state in relationship to the metal (it can not get any closer to the metal and its force is evenly dispersed, you do not have to deal with that force until you try to move sideways.
The field of attraction is still apparent when you try to move sideways on the metal but not as strong as trying to pull it straight off because most of the field is straight on and that is being taken care of by the contact of the two. You are only fighting the lines of force that are angled in the field until you reach the edge when the evenly distributed force is no longer canceled out by the metal-magnet contact. 
It's like sliding something heavy across a floor as opposed to picking it up and carrying across the room, sliding is much easier because you don't have to support all the weight, the floor is taking care of most of the work by supporting mass you are merely moving the mass on its support.      
A: For moving the magnet away from the steel plate, you need to use a force larger than the maximal force the magnet can provide under ideal conditions on this surface.
Note how you pull parallel to the magnetic field lines.
For moving the magnet sideways, you need a force stronger than its force in this direction. They will not be as strong as in the main direction of the magnet, but can still be very strong. But assuming the magnet is symmetric, we find that they all cancel out.  
So, when we move the magnet over the steel surface, we feel no magnetic force at all! What we feel is caused by the normal friction of magnet sliding on steel - just stronger, as it is proportional to the force of the magnet to the table.
