Attraction and repulsion of plates in capacitors

[hokhani]

If we make far away the two plates of an ideal parallel -plate-capacitor, which are connected to a battery, the stored energy decreased according to the energy consideration because capacity decreases while the voltage between the two plates is unchanged. Therefore, according to the energy considerations, the two plates like to go farther away towards the lower energy while on the other hand, they have opposite charge and we expect that they attract each other! Could anyone please tell me what practically happens if we release the two plates and why?

 

[Andrew Mason]

It would depend on a lot of factors, such as the voltage and how far apart the plates were and when you released them. Generally a capacitor will have either a physical structure that keeps the plates apart (air in-between as the dielectric) or a solid material dielectric that keeps the plates apart and insulated from each other. Otherwise, the plates would move toward each other and short circuit when they touched.

AM

 

[hokhani]

Otherwise, the plates would move toward each other and short circuit when they touched.

AM

Consider air as the dielectric between the two plates which are connected to a battery. with the consideration of energy, as I previously pointed, how the plates may become closer while the energy increases?

 

[Andrew Mason]

The battery is supplying energy to the capacitor. If you disconnect the battery with the plates holding charge Q, the voltage, and therefore the potential energy QV, will decrease as the distance between the plates is decreased. This is because the field E being constant, potential (V) decreases with distance. If you keep the battery connected, V remains constant (V=potential energy per unit charge = Ed) so as the separation decreases, the field and, therefore, plate charge increases. So the total energy (QV) increases. That energy is drawn from the battery.

AM

 

[hokhani]

The battery is supplying energy to the capacitor. If you disconnect the battery with the plates holding charge Q, the voltage, and therefore the potential energy QV, will decrease as the distance between the plates is decreased. This is because the field E being constant, potential (V) decreases with distance. If you keep the battery connected, V remains constant (V=potential energy per unit charge = Ed) so as the separation decreases, the field and, therefore, plate charge increases. So the total energy (QV) increases. That energy is drawn from the battery.

AM

Thanks. If you consider the battery and capacitor as one system, as a whole, and considering the fact that the systems like to go towards the lower energy potential, the plates like to become closer. To keep the plates in place, we would consume energy.
My question still remains:
We expect the two opposite-charged plates to attract each other while when the plates are connected to the battery, they like to become more separated!

 

[Andrew Mason]

Thanks. If you consider the battery and capacitor as one system, as a whole, and considering the fact that the systems like to go towards the lower energy potential, the plates like to become closer. To keep the plates in place, we would consume energy.

No energy is required to keep the charged plates in place. A force is required to keep them apart but this force does no work. However, if you move the plates closer together, the battery will act to increase the charge on the plates to maintain the potential energy per unit charge of the plate charges.

My question still remains:
We expect the two opposite-charged plates to attract each other while when the plates are connected to the battery, they like to become more separated!

This is not correct. The force between the plates is always attractive. With no battery keeping V constant, the force of attraction does not change as the plate separation changes. With the battery connected, the force of attraction between the plates increases the closer they get.

AM

 

[hokhani]

With the battery connected, the force of attraction between the plates increases the closer they get.
AM

Please check if I have got your reasoning correctly:
You mean that in the presence of the battery, when the two plates are closer, the increase of the energy stored in the capacitor is along with more battery consumption. So, the battery causes the two plates become closer.

 

[Andrew Mason]

Please check if I have got your reasoning correctly:
You mean that in the presence of the battery, when the two plates are closer, the increase of the energy stored in the capacitor is along with more battery consumption. So, the battery causes the two plates become closer.

The field E between the plates increases when d decreases because V = Ed is constant. So the force between the plates increases. Whether that brings the plates closer depends on the forces keeping them apart.

AM