Parallel Plate Capacitor with Dielectric Connected to a Battery

[physconomic]

Homework Statement

Represent the system as the superposition of a polarized dielectric slab and a vacuum capacitor to find the total electric field in the capacitor in terms of Q and the polarisation P. Then find the relationship between the displacement vectorD and Q.

Relevant Equations

Lorentz field? E=q/(A*sigma0)

Not sure how to set this question up or how to get to the second half

 

[berkeman]

Homework Statement:: Represent the system as the superposition of a polarized dielectric slab and a vacuum capacitor to find the total electric field in the capacitor in terms of Q and the polarisation P. Then find the relationship between the displacement vectorD and Q.
Relevant Equations:: Lorentz field? E=q/(A*sigma0)

Not sure how to set this question up or how to get to the second half

That's not really the full problem statement, and a diagram would help, but it sounds like you have a parallel plate capacitor with a dielectric slab filling some fraction of the separation distance?

If so, just model it as two capacitors in series -- one with the dielectric in it, and one with vacuum. Once you do that, just use the traditional equations for the charge on a capacitor versus voltage and capacitance, and the equation for the series combination of capacitors...

 

[physconomic]

That's not really the full problem statement, and a diagram would help, but it sounds like you have a parallel plate capacitor with a dielectric slab filling some fraction of the separation distance?

If so, just model it as two capacitors in series -- one with the dielectric in it, and one with vacuum. Once you do that, just use the traditional equations for the charge on a capacitor versus voltage and capacitance, and the equation for the series combination of capacitors...

Hi sorry yes it's just a standard parallel plate capacitor with a linear dielectric material filling the whole gap. Thank you though.

 

[berkeman]

Okay, so can you start working the problem and post your work? You can also do a Google search for more information and examples -- this is a very common intro question about capacitor calculations...