Dielectrics

Question 1

What is a dielectric?

Answer 1

> It is an insulator

> Changes the electric field passing through it by becoming polarised

Question 2

How are dielectric used?

Answer 2

> Capacitors are designed to work at different frequencies and the dielectric chosen is important to enable this.
They change the capacitance of a capacitor
Increase the electrical breakdown field between high-voltage conductors:

Question 3

What is the relative permittivity?

Answer 3

This is a constant for a material and is dependent on the frequency of the changing electric field

Question 4

What is the equation for the capacitance of a capacitor?

Answer 4

Capacitance = Charge stored / Volt

Question 5

How is the relative permittivity of a dielectric calculated?

Answer 5

Calculating the capacitance without the dielectric: C0 = Q0/V
Calculating the capacitance with the dielectric: C = Q/V
To calculate the relative permittivity you compare the two capacitances.
εr = Q/Q0 = C/C0

Question 6

What happens when a dielectric is placed in an electric field?

Answer 6

It is an insulator so the charges do not flow within the material but they do shift a bit from their equilibrium position causing the material to become polarised.

Question 7

What is polarisation?

Answer 7

> Occurs in a medium when the positive and negative charges are displaced relative from their equilibrium position
The opposite surface of a dielectric acquires the opposite surface charge densities that are related to the polarization in the medium

Question 8

What is the electric dipole moment?

Answer 8

It is kind of like the magnitude of the polarization

Question 9

What is the equation for the electric dipole moment?

Answer 9

P = Qa
Where a is the separation between the positive and negative charges in the dielectric.
The dipole moment and separation are both vectors with a direction: P ⃗ = Qa ⃗

Question 10

How is the distance ‘a’ and dipole moment ‘p’ defined for the polarisation of a material?

Answer 10

From NEGATIVE TO POSITIVE

Question 11

Even though the charges are separated by distance ‘a’ the overall net charge is….
but unless….

Answer 11

….zero

….the charges are at the same point then there will be a dipole moment

Question 12

How is this movement of charge causing polarisation applied to a dielectric material atomically?

Answer 12

For an atom with a positive nucleus and circular cloud of electrons the overall point of positive and negative charge are at the same point.
When placed into a magnetic field the centre point of the negative electron cloud moves from the centre point of the positive nucleus. The distance moved is ‘a’

Question 13

How can an unpolarised material become polarised?

Answer 13

When placed into a magnetic field

Question 14

How can the induced polarisation be calculated? What is the equation? What is the constant?

Answer 14

Pinduced = αE
α = Polarizability of the material

Question 15

For neutral atoms what is the polarizibility constant?

Answer 15

αe = Electronic polarization (for electrons)

Question 16

What happens when a dielectric is placed within a capacitor?

Answer 16

The dielectric becomes polarized and the capacitance changes

Question 17

What is going on within the dielectric in a capacitor?

Answer 17

> Inside the centre, the charges cancel out and so the inside of the dielectric is effectively neutral
The edges of the dielectric becomes charged because it does not cancel (surface polarization)

Question 18

When a battery is connected to the capacitor with the dielectric in it, how does the polarisation change and which direction is the electric field and which direction is ‘a’ ?

Answer 18

> One plate on the capacitor is positive
One plate on the capacitor is negative
The electric field is from positive to negative
The polarisation is such that on the surface the negative side is by the positive plate and positive side is by the negative plate
a is in the same direction as the electric field

Question 19

What are the two symbols for dipole moment and polarisation?

Answer 19

p = dipole moment
P = polarisation

Question 20

How are dipole moment and polarization related?

Answer 20

Polarisation = Sum of dipole moments / Unit of volume

Question 21

What are the equations to calculate the polarization from dipole moments?

Answer 21

P = (1/Volume)×(p1+p2+p3+…+pN)
P = n×Pavg
Where n = Number of charges per volume

Question 22

What is surface charge density?

Answer 22

This is the number of charges per unit of area

Question 23

What is the equation for surface charge density?

Answer 23

σ = Q/A

surface charge density = surface charge / area

Question 24

How can the charge of the whole dielectric be modelled? What is the equation for this?

Answer 24

> As one large dipole moment
ptotal = Qd
Total dipole moment = surface charge × length of dielectric

Question 25

If we know the overall dipole moment how can we then calculate the polarizibility?

Answer 25

P = ptotal/volume
P = Q×d/Volume

Question 26

What can be related between surface charge density and polarizability? What is the equation for this?

Answer 26

They are the same

> P = Q×d/Volume = Q×d/A×d = Q/A = σ

Question 27

What differentiates polarization and surface charge density?

Answer 27

polarization is a vector and is perpendicular to the surface charge

Question 28

What is electric susceptibility? What is its symbol?

Answer 28

> It is a proportional constant relating electric field strength to Polarization
Symbol: Xe

Question 29

What is the equation for electric susceptibility?

Answer 29

Xe = nα/ε0

Question 30

What are the equations used to calculate the polarizability using the electric susceptibility constant?

Answer 30

P = Xe × ε0 × E

Question 31

What is the Clausius-Mossotti equation?

Answer 31

This relates macroscopic to microscopic
εr-1 / εr+2 = nα / 3ε0
[YOU DONT NEED TO REMEMBER THIS BUT NEED TO KNOW HOW TO USE IT]