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Scenario: Players are fighting an invisible beholder and its Antimagic Cone. One player, with high passive perception, wishes to check to see if they are being effected by the cone every five feet they move.
Question: How often can the PC check with their passive perception during combat?
You can't make Passive perception checks. Passive perception is what you use when you don't roll any checks; it's the baseline enemies need to beat when trying to hide from you.
In the anti-magic cone situations, the player doesn't check anything. If the beholder is hidden (because its stealth check exceeded the player's passive perception) then the player will not be able to find it.
Whether or not the player detects walking into the anti-magic cone depends on whether something obvious happens when they step into it. For example, if they have a Ioun stone, then they will obviously notice the thing falling to the ground. This does not depend on Passive Perception. On the other hand, if they have no visible magical effects on them, they might not realize that they stepped into an anti-magic field at all.
If the player wants an extra chance of finding where the Beholder is, they can make an active Perception check. That allows them to roll a normal Perception check (not use their passive) but since it requires an Action, they can probably only do that once on their turn. And it still won't help them in finding out about the anti-magic field.
The passive Wisdom (Perception) check only comes into effect when the DM chooses, with the two cases laid out in the rules being repeated tests or when the DM wishes to conceal information.
A passive check is a special kind of ability check that doesn't involve any die rolls. Such a check can represent the average result for a task done repeatedly, such as searching for secret doors over and over again, or can be used when the DM wants to secretly determine whether the characters succeed at something without rolling dice, such as noticing a hidden monster.
--- Player's Handbook p. 175
When a player character is actively searching they should take the Search action, and a success should probably tell them where the Beholder (assuming it is hidden), or its antimagic cone is.
When you take the Search action, you devote your attention to finding something. Depending on the nature of your search, the DM might have you make a Wisdom (Perception) check or an Intelligence (Investigation) check.
--- Player's Handbook p. 193
At all times all creatures, including PCs, are using their passive Perception to notice things. That can be walls, doors, treasure chests, or invisible beholders.
Passive Perception serves as the minimum Perception that a creature has at any time.
You can make any kind of check using your normal action, but you can also use the Search action to try and roll better than your passive Perception. Even if you roll a 1, your passive Perception is still on.
However, this won't really help with seeing an invisible beholder, nor locating an anti-magic field.
An invisible creature is invisible, you can't see them. You can't just roll high on Perception and see the invisible. But they are probably still making noise, interacting with the environment, and doing things that let you know their location. Knowing that, you can either attack with disadvantage, or dispel the invisibility.
If the beholder hides, then they can act stealthily to become even less detectable. However, a canny player can use the Search action to attempt to locate the beholder. But that still won't make the beholder visible.
Perception is a mundane sense; you can't use it to see magic. You need to use spells or abilities that let you detect magic.
Your DM may allow you to use passive Arcana or make an Arcana check to detect the magic if you are lucky. Or they could rule that since the cone comes from the eye, a PC can figure out roughly where the cone is. These seem like pretty reasonable rulings to me.
