How far does trap searching (Passive or Active) extend? I.E If PCs enter a 30x30 room, and the perception beats the DC of a trap on the other side of the room do they see it?
Passive perception checks are made when the DM knows that the PCs are in a position to notice something and wonders if they actually do. This will depend on the trap. Obviously, if the trap is not yet visible from where a PC stands, it doesn't matter how close they are – they don't get a roll or passive check yet.
This is covered in the DMG (original printing, p. 85, emphasis added):
When the party is within line of sight of a trap, compare each character's passive Perception check with the DCs of the traps in the room.
Active perception checks are no different than passive checks in this regard: if something could be noticed from where they are making the check then a check will indicate whether they do notice it; if nothing could be noticed from where they stand then the roll isn't going to give them magic x-ray vision.
There is no concept of a "search area" for trap detection that's similar to earlier editions. You either have line of sight on some component of a trap or you don't, and there's no spending an hour searching the floor, each of four walls, and the ceiling of a 10' by 10' room in this edition. You can conduct a search of an area with Perception, but this isn't any different than an active Perception check standing still (unless the DM opts to give a "thoroughness bonus" or somesuch).
Finally, as a guide for what should be possible for a check to notice, consider this guidance from the "Dispensing Information" section of the DMG (p. 26):
Hazards, Traps, and Obstacles: ... If the PCs can sense a hazard or obstacle, you should emphasize that element. It's better for the game if the PCs sense hints of impending danger. ... [K]nowing that something might be dangerous actually builds tension and fun. A hazard that springs out of nowhere has none of that appeal.
Hinting at dangerousness (though not specifically that the danger is a trap), is good for the game. It gets your players engaged and working the problem creatively. Even if they don't make their Perception checks (especially if they don't), they will be on alert, perhaps even worried, and you'll be seeing a much more entertaining moment at the table. A danger (and its consequences) that is actively engaged with and therefore chosen by the players is way, way more fun for everyone than a danger that just jumps out, numerically inconveniences the group, and then is gone.
A PC's sight range is so long as to be unimportant, however seeing a concealed trap from 30 squares vs 10 squares away should probably be more difficult, especially w/passive perception. Active perception Checks probably shouldn't face this limitation but to balance endless dice rolling I would have the PC in question be forced to move closer to where they are looking. A good rule of thumb is to always give the PCs at least one roll (even if passive) before they enter the trap trigger range. For example. (A PC's mini/token is being moved. You say, "As you're walking roll your passive perception" if the PC detects the trap "You pull yourself short sensing something is wrong" or if they fail "You hear a mechanical click as a trap triggers"
Generally the best way to spice up trap searching is to make players declare what they are looking at (the more things the more time it takes) and have a ticking time bomb, be it a nasty monster (such as a minotaur in the labyrinth) or something like the dungeon is flooding to egg them onward.