Question about capacitors with dielectrics

[anon6912]

Say i have a capacitor and i supply it with a voltage V and after that it has charge density sigma_initial on each plate.

Now i remove the voltage source and then introduce a dilectric with area A that it equal to the area of one of the plates in the capacitor to the capacitor.

But this dielectric is only touching one plate.

My question is: is the net charge density on each plate(sigma_initial - sigma_induced) the same in both plates or different?

please explain...

 

[sophiecentaur]

I think the answer is that the same charge is there but the molecules in the dielectric have all polarised a bit. This has increased the capacity ov the capacitor. Equivalent to moving the plates closer together. Now
Q=CV
so the voltage will have dropped. As for the energy difference, some work has been done in moving the dielectric into place- nothing violated either way, I think.

 

[Bob S]

Hi Anon-
Sophie is correct. Charge is conserved, and the charge distribution is unchanged. The stored energy is

E = Q²/2C

So when the dielectric is pulled (not pushed) in, the stored energy drops, and work is done.

Bob S

 

[sophiecentaur]

Yes- the same work that the plates would do if they were allowed to come together and have the equivalent capacitance.