Capacitors Concept Page - 5

Definition

Properties of Dielelctrics

1. Dielectrics does not have any free charges.
2. When an electric field is applied there is small displacement of bound charges creating small  electric dipoles within the dielectric. This phenomenon is called Polarization. 
3. The electric field inside and outside a dielectric gets modified due to presence of dipoles.
4. Dielectrics can store energy.

Formula

Energy in the electric field in a dielectric

U=12CV2=12Kϵ0AdV2$U={\displaystyle \frac{1}{2}}C{V}^2={\displaystyle \frac{1}{2}}{\displaystyle \frac{K{ϵ}_{0}A}{d}}{V}^2$
where K$K$ is the dielectric constant

Definition

Electric polarization of matter

Polarization occurs when an electric field distorts the negative cloud of electrons around positive atomic nuclei in a direction opposite the field.  By inducing the movement of electrons within an object, one side of the object is left with an excess of positive charge and the other side of the object is left with an excess of negative charge. Charge becomes separated into opposites.The polarization process always involves the use of a charged object to induce electron movement or electron rearrangement.

Definition

Permittivity and relative permittivity

E=E0K$E={\displaystyle \frac{E_0}{K}}$
where K$K$ is the relative permittivity,E$E$ is the resultant electric field and E0$E_0$ is the applied electric field. 
The permittivity is ε=ϵ0K$\epsilon ={ϵ}_{0}K$

Formula

Electric field due to a point charge placed in an infinite dielectric

E=q4πϵ0r2K$E={\displaystyle \frac{q}{4\pi {ϵ}_0{r}^{2}K}}$
where q$q$ is the point charge placed inside an infinite dielectric and r$r$ is the distance at which the electric field is calculated.

Definition

Dielectric strength

The maximum electric field that a dielectric medium can withstand without breakdown (of its insulating property) is called its dielectric strength.
For air, it is 3×106 V/m$3\times {10}^{6}V/m$
This puts a restriction on the value of capacitance of a given size and is the reason why capacitors are in the range of μF$\mu F$. 

Definition

Effect of dielectric on capacitance

The larger the dielectric constant, the more charge can be stored. Completely filling the space between capacitor plates with a dielectric increases the capacitance by a factor of the dielectric constant
C = KC'
Where C= New capacitance after introduction of dielectric
C' = Capacitance with no dielectric between the plates.

Definition

Dielectric

Dielectrics are non-conducting substances which are the insulating materials and are bad conductor of electric current.Mica, Plastics, Glass, Porcelain and Various Metal Oxides and even dry air is also example of dielectric.

Definition

Dielectric Constant

n parallel plate capacitor, when dielectric slab is placed between the two plates then the ratio of the applied electric field strength to the strength of the reduced value of electric field capacitor is called dielectric constant that is:
K=EoE$K={\displaystyle \frac{E_o}{E}}$
K = Dielectric constantEo=Dielelctric$E_o=Dielelctric$
E = Net Field

Definition

Non-polar dielectric

If in a substance the centre of positive charge and centre of negative charge of each molecule coincide with each other, because of symmetry of molecules, then these substances are called non-polar dielectric substances.
Ex: N2,O2,H2$N_2,O_2,H_2$ etc.

Definition

Polar dielectric

If in any dielectric substance the centre of positive charge and centre of negative charge of each molecule do not coincide, then such type of dielectric material is called polar dielectric.
Ex : water and HCl 

Definition

Induced surface charge density and polarization in dielectric

Induced surface charge density is given by:
σP=P⃗ .n^${\sigma }_P=\overrightarrow{P}.\hat{n}$
where 
P⃗ :$\overrightarrow{P}:$ Polarisation
n^:$\hat{n}:$ Unit vector along the outward normal surface

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