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My question is, does an electrically charged material attract dust?

Would it be possible to make a device like a vacuum cleaner based on a mechanism like this (in principle)?

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Do you mean this kind of device: ? – Qianyi Guo May 2 '14 at 14:15
@GuoQianyi that looks exactly like what OP is looking for! If you could write a bit more about the mechanism of operation, you could (and should) post it as an answer! – Danu May 2 '14 at 14:43
I am wondering whether a device similar to ( can be built except instead of a vacuum for cleaning, the device uses some sort of electricity to attract the dust. – user45705 May 2 '14 at 16:07

An electrostatic precipitator (ESP) is a highly efficient filtration device that removes fine particles, like dust and smoke, from a flowing gas using the force of an induced electrostatic charge minimally impeding the flow of gases through the unit. [1]

Conceptual diagram of an electrostatic precipitator Credit: (CC-BY-SA 3.0)

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If you have a polarizable material (like a dust mote) in an electric field, your material will develop an electric dipole moment.

An electric dipole in an electric field feels a force $\vec F = -\vec\nabla(\vec d \cdot \vec E)$. This has the net effect of attracting polarizable objects to regions of stronger electric field.

There are filtration systems that are based on this phenomenon (as indicated in a comment on your question), but your design must take into account that the strength of the force falls off very quickly with distance.

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