## Introduction

Hello it's a me again Drifter Programming!

Today we continue with **Electromagnetism **to get into **Dielectric materials** that are placed in-between of the two conductive plates of capacitors!

All the mathematical equations will be drawn using quicklatex!

So, without further do, let's get straight into it!

## Quick Recap

Till' now we supposed that the space between the two parallel conductive plates of a capacitor is a vacuum and so doesn't contain anything!

Last time we even found an equation that gives us the energy density u and this equation contained the (dielectric) permittivity of vacuum (ε0) which was:

I mentioned that this equation will be true for any conductor...

So, what exactly do we put in-between of the two plates of a capacitor?

## Dielectrics

The materials in-between of those plates are called Dielectrics.

Dielectrics are **non-conductive materials** and so **insulators **of electricity.

A **common type of capacitor** is build up of long stripes of metal sheets that are separated by plastic stripes (for example Mylar). Such a capacitor is very small, but has a "large" capacity of some μF and so is very useful for a lot applications!

Here you can see **how such capacitors are basically build up**:

**Electrolytic capacitors** are also a very interesting type of capacitor!

They use a very thin layer of insulative oxide in between of a metal plate and a conductive solution.

We know that the capacitance C is inverse proportional to the distance d between the plates of a capacitor, because:

Because of that electrolytic capacitors of relatively small size have a capacitance of 100 up to 1000μF!

Here you can see the **basic principle** of such capacitors:

There are basically** 3 reasons for which we need and use dielectrics**:

- They
**solve the mechanical problem**of restraining large metal plates in place with a very small distance in-between of them so that they don't contact. We basically separate them using such materials. - Dielectric materials "suffer" of
**Dielectric**(or Electrical)**Breakdown**, which means that**they become electrically conductive**after the current that flows through them exceeds their breakdown voltage. They basically become conductors of electricity and can even withstand stronger electric fields. Each dielectric material has a dielectric strength (We will get back to this later on). - The
**capacitance**of a capacitor**is larger****when there is a dielectric material**, when comparing it to air or vacuum.

Let's now get into the properties of Dielectrics...

## Dielectric constant (relative permittivity)

Let's say that the initial capacitance of a capacitor is given by:

and that the capacitance when having a dielectric material is:

The charge Q in both cases is of course the same, but the "new" voltage V is smaller then the initial voltage V0, cause as told before the "new" capacitance C is of course greater then the initial capacitance C0.

The ratio C by C0 (equal to V0 by V) is defined as the **dielectric constant** or relative permittivity **of a dielectric material** and is noted as K (or εr):

We can get into the **conclusions**:

- the capacitance is increasing by factor K, while potential is decreasing by factor K.
- K is a "clear" number greater then 1, cause C is always greater than or equal to C0.
- Of course K = 1 for a vacuum.

## Dielectric permittivity

Let's say we want to decrease an electric field E0 by factor K then the new electric field E will of course be:

This means that **a dielectric material decreases the electric field** or **decreases the energy density of charge**. Of course the surface charge density of the conductors doesn't change, but opposite charge inducts on each side/surface of the dielectric material. These inductive charges are caused by the reallocation of charge inside of the dielectric material, something called **polarization**!

The **inductive charge is **of mostly **proportional to the electric field E **inside of the dielectric material, where **the dielectric constant K is characteristic for each material**. When having very strong electric fields or unstable materials then things change, but let's only talk about the "simple case".

Let's find a **relation between the inductive charge and charge on the surface of the plates**.

Let's represent the surface charge density as σ for the capacitor and σi for the dielectric material specifically. The total surface charge density on each plate of the capacitor is: *(σ - σi)*.

The electric field E between the plates is calculated using the total surface density and so:

When having a dielectric material this becomes:

Using those equations we end up with **an equation that calculates the inductive charge density σi** using the total charge density σ and dielectric constant K, which is:

This equation shows us that if K is very big than σi is almost as big as the total charge density σ! In such a case the density σi cancels out the total charge density σ and so the electric field and potential difference become a lot smaller then the values that we have in a vacuum!

The** product k*ε0** is called **permittivity **of the dielectric material and is** represented by ε**.

Using the permittivity ε the **electric field E** now is:

And the** capacitance when having a dielectric material** is given by:

When in a vacuum then K = 1 and so ε = ε0. The value **ε0 is called vacuum permittivity **or **electric constant**!

Redoing the prove of last time we can now end up with the **energy density u when having dielectrics** which is:

And so supposing that the charge of each plate stays the same, the value of εo gets multiplied by the factor K, which means that the electric field E decreases by factor 1/K and so does the energy density u. The remaining energy goes to the "outer" electric field that we previously never took into our calculations. We will not need this in our "simple" examples, but either way it's interesting to know what happens!

## Dielectric strength

We previously said that any dielectric material that a strong electric field is applied to becomes conductive and we called this phenomenon **Dielectric Breakdown**.

The **maximum electric field or voltage that a material can withstand** defines the **dielectric strength** of it. This means that the material "breaks appart" after getting such a strong field applied.

This value is strongly dependent of:

- temperature
- mixture "scents"
- small anomalies
- metal electrodes
- and more...

This means that we can only give** approximate values** to the dielectric strength of materials!

Here a **table **of some dielectric strengths and constants of common materials:

## How to solve problems around Dielectrics

Solving problems that contain dielectrics is not very difficult.

Here some **tips**:

**1)** Always use the **correct metrics **(like I say every time):

- meters (m) for distances (they will never be directly meters, but mostly cm)
- N/C or V/m for electric field magnitude (whatever is easier)
- C^2/N*m^2 or F/m for permittivity (ε0 mainly)

**2) **There is a **flood of equations **that apply to Electromagnetism:

- always ask yourself what each symbol represents.
- learn to distinguish charges and charge densities and also electric fields and potentials.
- remember that the capacitance of a capacitor with dielectrics is greater then the one without a dielectric material.
- the inductive charge density σi in the dielectric material is always smaller then the charge density σ of the plates of the capacitor.
- When the charge Q of the plates is given then the electric field and potential difference decrease in the presence of a dielectric material when compared to the absence.

Examples/Exercises next time!

## Previous posts about Physics

**Intro**

Physics Introduction -> what is physics?, Models, Measuring

Vector Math and Operations -> Vector mathematics and operations (actually mathematical analysis, but I don't got into that before-hand :P)

**Classical Mechanics**

Velocity and acceleration in a rectlinear motion -> velocity, accelaration and averages of those

Rectlinear motion with constant accelaration and free falling -> const accelaration motion and free fall

Rectlinear motion with variable acceleration and velocity relativity -> integrations to calculate pos and velocity, relative velocity

Rectlinear motion exercises -> examples and tasks in rectlinear motion

Position, velocity and acceleration vectors in a plane motion -> position, velocity and accelaration in plane motion

Projectile motion as a plane motion -> missile/bullet motion as a plane motion

Smooth Circular motion -> smooth circular motion theory

Plane motion exercises -> examples and tasks in plane motions

Force and Newton's first law -> force, 1st law

Mass and Newton's second law -> mass, 2nd law

Newton's 3rd law and mass vs weight -> mass vs weight, 3rd law, friction

Applying Newton's Laws -> free-body diagram, point equilibrium and 2nd law applications

Contact forces and friction -> contact force, friction

Dynamics of Circular motion -> circular motion dynamics, applications

Object equilibrium and 2nd law application examples -> examples of object equilibrium and 2nd law applications

Contact force and friction examples -> exercises in force and friction

Circular dynamic and vertical circle motion examples -> exercises in circular dynamics

Advanced Newton law examples -> advanced (more difficult) exercises

**Electromagnetism**

Getting into Electromagnetism -> electromagnetim, electric charge, conductors, insulators, quantization

Coulomb's law with examples -> Coulomb's law, superposition principle, Coulomb constant, how to solve problems, examples

Electric fields and field lines -> Electric fields, Solving problems around Electric fields and field lines

Electric dipoles -> Electric dipole, torque, potential and field

Electric charge and field Exercises -> examples in electric charges and fields

Electric flux and Gauss's law -> Electric flux, Gauss's law

Applications of Gauss's law (part 1) -> applying Gauss's law, Gauss applications

Applications of Gauss's law (part 2) -> more Gauss applications

Electric flux exercises -> examples in electric flux and Gauss's law

Electric potential energy -> explanation of work-energy, electric potential energy

Calculating electric potentials -> more stuff about potential energy, potential, calculating potentials

Equipotential surfaces and potential gradient -> Equipotential surface, potential gradient

Millikan's Oil Drop Experiment -> Millikan's experiment, electronvolt

Cathode ray tubes explained using electric potential -> cathode ray tube explanation

Electric potential exercises (part 1) -> applications of potential

Electric potential exercises (part 2) -> applications of potential gradient, advanced examples

Capacitors (Condensers) and Capacitance -> Capacitors, capacitance, calculating capacitance

How to solve problems around Capacitors -> combination, solving problems, simple example

Electric field energy and density -> Electric field energy, energy density

## REFERENCES:

- Dielectric: https://www.britannica.com/science/dielectric
- Electrolytic capacitor: https://en.wikipedia.org/wiki/Electrolytic_capacitor
- Electrical Breakdown: https://en.wikipedia.org/wiki/Electrical_breakdown
- Relative permittivity: https://en.wikipedia.org/wiki/Relative_permittivity
- Vacuum permittivity: https://en.wikipedia.org/wiki/Vacuum_permittivity
- Dielectric strength: https://www.elandcables.com/the-cable-lab/faqs/faq-what-is-dielectric-strength

And this is actually it for today and I hope that you enjoyed it!

Be happy, cause next time we will get into exercises around capacitors!

Bye!