Why is black soot coming from my electric heating vents?

electric heating

We have two AC/heating systems. One is fine, the other (over time of 2 months) has a black sooty residue collecting where the air blows out. This unit has the vents in the ceiling. Will filters help? Where should they go? In the return or in the room vents?

The soot seems to be in the air because if I close the bedroom door closest to the heating unit, the black soot gets on the carpet under the door.
There is a 20×20 filter in the return……as it should be, but the soot collects anyway. I even tried one of those Arm & Hammer ones that are suppose to trap allergens and more dust than the spun fiberglass ones. I couldn’t tell that it did any better.

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