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A capacitor is usually formed by an insulater between two conductive plates. By applying voltage difference between the plates we create an electric field within the insulator in one direction. If you are not familiar with the concept please watch this video.

But! If I introduce two extra conductive plates to a normal capacitor as below drawing:

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Moreover, If I apply the voltages Vx=A.sin(wt) and Vy=A.cos(wt), could I get a constant magnetic field towards z+? If not why? Thanks.

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In a capacitor, you apply a voltage between the plates. This creates an electric field between the plates.

A dielectric has neutral molecules that are + on one end and - on the other. An electric field pulls the + and - ends in opposite directions, which can line up the molecules parallel to the field. The orientation lasts as long as the electric field is present. See this post

You can do similar things with a magnetic field. Each iron atom is a small magnet. Normally they point equally is all directions. But if you put iron in a magnetic field, they tend to line up parallel to the field. The piece of iron temporarily becomes magnetized as long as the magnetic field is present. You can create the magnetic field by putting the iron next to one pole of a permanent magnet or by putting it in a solenoid.

This isn't directly answering your question, but it is related and perhaps of interest. Some materials are piezoelectric or electrostrictive. That is, squeezing the material can orient charges and generate an electric field.

There are also magnetostrictive materials, such as TbFe2 or DyFe2. Squeezing these generates a magnetic field.

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