# Intensity of polarization vector of a plate capacitor

• gruba
In summary: And remember, the goal is to get better and better at solving problems.In summary, the intensity of polarization vector P of a dielectric in the first stationary state is 318.6 nC/m2.
gruba

## Homework Statement

Plate capacitor with distance between plates 'd=4mm' is fully filled with homogeneous linear dielectric. Capacitor is connected to the source of DC voltage, first stationary state is established, then the capacitor is separated from DC voltage source. After that, dielectric is fully eliminated from capacitor and new stationary state is established. Difference between voltage in second and first stationary state is '(delta)U=144V'. Calculate intensity of polarization vector 'P' of a dielectric in the first stationary state (capacitor is separated from DC voltage source, and dielectric is not eliminated).

## Homework Equations

((integral)DdS)=Q
D=e0E+P
(delta)U=U2-U1

## The Attempt at a Solution

Law of conservation of charge is valid, so Q=const.
In the first stationary state, we have a plate capacitor with dielectric, so we use Gauss law for dielectrics:
((integral)DdS)=Q
D=Q/S=e0E+P (1)
In the second stationary state, we have a plate capacitor without dielectric (vacuum), so we use Gauss law for vacuum:
((integral)EdS)=Q/e0
e0E=Q/S (2)
Combining (1) and (2) gives
P=e0(E0-E)=e0*(delta)U/d
I get the intensity of polarization vector P=318.6 nC/m2
What puzzles me is that we need to find intensity of polarization vector in the FIRST stationary state, so we need to find voltage U1 in that state? Also, is there intensity of polarization vector if there are no dielectrics?

Thanks.

What puzzles me is that we need to find intensity of polarization vector in the FIRST stationary state, so we need to find voltage U1 in that state? Also, is there intensity of polarization vector if there are no dielectrics?
... there is no polarization without a dielectric to be polarized.
You do not need to know U1, as you discovered, because you know the difference in voltage between the states, but you can calculate it if you like.

Simon Bridge said:
... there is no polarization without a dielectric to be polarized.
You do not need to know U1, as you discovered, because you know the difference in voltage between the states, but you can calculate it if you like.

Could you please tell if intensity of polarization vector in the first stationary state is

P=-e0*U1/d

or

P=e0*(delta)U/d

Which result is correct and why? Also, how to calculate U1?
If P=P1+P2, P2=0 because there is no dielectric, right?

Last edited:
gruba said:
.
I will rush in where angels fear to read and state that the problem is unsolvable.
EDIT: solvable!
Hint: D = ε0E1 + P = ε0E2
You know E2 - E1 from knowing V2 - V1.

Last edited:
Simon Bridge
Relationship between electric displacement and the voltage for a parallel-plate capacitor?

Simon Bridge said:
Relationship between electric displacement and the voltage for a parallel-plate capacitor?
Could you tell if P=318.6 nC/m2 is correct or not and why?

gruba said:
Could you tell if P=318.6 nC/m2 is correct or not and why?
I can tell, and it's correct! Even the units. Congrats!

gruba
I don't normally comment on if an answer is correct or not.
Anyway - what if I say it is wrong? How do you know I have got it right and the rude man is not wrong again?

You are training to solve problems that nobody knows the answer to - if you get really good, you'll be solving problems nobody has even thought of yet - who will you ask then?

Bit severe, what?

Yes, once at work as a scientist or engineer you won't know the answers a priori. But by then you will hopefully have learned how to get them. As a student, by definition you still don't have that knowledge.

Which is why the typical textbook has numerical or other answers to all the odd or even problems, and why instructors are there to provide answers also. And why I make it a practice, time permitting, to have a numerical answer at hand should the OP want to compare with his/hers. If the answers don't agree I don't offer a guarantee mine is right but it usually is, thank you. Textbook answers have been known to be wrong also; we had an example here not long ago. Doesn't lessen their value.

Bottom line: don't expect perfection. We're all human.

Tanya Sharma

## What is the intensity of polarization vector of a plate capacitor?

The intensity of polarization vector of a plate capacitor refers to the strength of the electric field created by the separation of positive and negative charges on the plates of the capacitor.

## How is the intensity of polarization vector of a plate capacitor calculated?

The intensity of polarization vector is calculated by dividing the magnitude of the charge on one plate by the distance between the plates.

## What factors affect the intensity of polarization vector of a plate capacitor?

The intensity of polarization vector can be affected by the distance between the plates, the magnitude of the charge on the plates, the dielectric constant of the material between the plates, and the voltage applied to the capacitor.

## What is the unit of measurement for intensity of polarization vector of a plate capacitor?

The unit of measurement for intensity of polarization vector is volts per meter (V/m).

## How does the intensity of polarization vector affect the capacitance of a plate capacitor?

The intensity of polarization vector is directly proportional to the capacitance of a plate capacitor. This means that as the intensity increases, the capacitance also increases.

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