# Parallel Plate Capacitor with Dielectric Connected to a Battery

• physconomic
In summary, the question asks for the total electric field in a parallel plate capacitor with a polarized dielectric slab and a vacuum capacitor. This can be found by modeling the system as two capacitors in series and using the traditional equations for charge, voltage, capacitance, and the series combination of capacitors. The relationship between the displacement vector D and Q can also be found using these equations and by solving for Q.

#### 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

physconomic said:
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...

berkeman said:
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.

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...