Push the dielectric half way into the capacitor

[indigojoker]

This is a general question because I cannot find any example problems to base this question off of.

Suppose we have two parallel plate capacitors, what work is needed to push the dielectric half way into the capacitor and why does the slab feel a pull into the capacitor?

 

[learningphysics]

The force due to the electric field acts in a direction that decreases stored energy... the capacitor with the dielectric has less energy than the capacitor without the dielectric... so the force acts in a way that pulls the slab in (decreasing stored energy).

what happens is that the dielectric gets polarized and is attracted by the capacitor charges, pulling it in.

 

[indigojoker]

why does the field act in a direction that decreases stored energy?

And how does one calculate the work done to push the dielectric into the capacitor?

W=Fd, what would be the F=Eq? Not sure where to go from here

 

[learningphysics]

Work done is final energy - initial energy.

What is the initial energy in the capacitor before the slab is put in?

What is the final energy? For this part think of it as 2 capacitors... each with half the area, and each with a charge of (1/2)Q. what is the energy on each capacitor? what is the sum?

The work done will be negative.

 

[indigojoker]

why does the electrostatic energy decrease when a dielectric is inserted? (assuming that the plates are not connected to a battery)

 

[learningphysics]

why does the electrostatic energy decrease when a dielectric is inserted? (assuming that the plates are not connected to a battery)

Energy = Q^2/(2C)

charge is fixed. capacitance goes up, so the energy goes down.

 

[indigojoker]

but what is the point of the dielectric if the energy decreases?

 

[learningphysics]

but what is the point of the dielectric if the energy decreases?

I think there are many applications of dielectrics, not related to energy.