Monday, February 10, 2020

Unizor - Physics4Teens - Electromagnetism - Electric Field -Permittivity

Notes to a video lecture on http://www.unizor.com

Electric Permittivity

Let's take a closer look at Coulomb's Law
F = k·qA·qB / R²
where
F is the magnitude of the force of attraction (in case of opposite charges) or repelling (in case of the same type of charge, positive or negative) in N - newtons
qA is electric charge of point-object A in C - coulombs
qB is electric charge of point-object B in C - coulombs
R is the distance between charged objects in m - meters
k is a coefficient of proportionality (Coulomb's constant) equals to 9.0·109 in N·m²/C²

The intuitive explanation of the inverse proportionality of this force to a square of a distance between objects A and B was that the force emitting by an electric point-charge is distributed around it in a radial fashion and, at distance R, should be inversely proportional to an area of a sphere of the radius R.
The area of a sphere of radius R is 4πR². Therefore, it's more natural to express Coulomb's with 4πR² in the denominator. Then it will look like this
F = qA·qB / (4π·ε0·R²)
where
ε0 is a constant called permittivity of vacuum.
In terms of Coulomb's constant k it is equal to
ε0 = 1/(4π·k) = 8.85419·10−12
measured in C²/(N·m²)

In the above definition permittivity is the property of space between the charges to let the force of electric field through. It is analogous to such mechanical properties as resistancefrictionviscosity.

As experiments show, the same electric charges at the same distance but in different environments produce electric fields of different intensities.
Environment matters. In vacuum a specific point-charge at a specific distance produces the field of one intensity, while, positioned inside a sand box, the same charge at the same distance would produce a field of different intensity.

That's why we specifically called ε0 the permittivity of vacuum, as no other environment was considered. All the experiments described before relate to vacuum as the media where these experiments are conducted. In different environment the force of electric field would differ.

This prompts us to introduce an absolute permittivity εa (or simply ε) of any media and its relative permittivity εra0.
The relative permittivity of a media is also called its dielectric constant with the value of this dielectric constant for vacuum being equal to 1.
For olive oil the dielectric constant is 3, for silicon its about 11-12, for mineral oil its about 2, for marble - 8, for titanium dioxide - between 86 and 173 etc.

Now the formula for intensity of electric field in a media with relative permittivity εr looks like this
F = qA·qB / (4π·εr·ε0·R²)
So, generally speaking, when the electric field speads into any media with a dielectric constant εr, we should use the coefficient / (4π·εr·ε0) instead of Coulomb's constant k.

The greater the value of the dielectric constant - the stronger it resists to penetration of electric field, so the field is weaker than in vacuum for the same charge and distance. Vacuum is the easiest for the electric field to penetrate.

Also worth noting that the permittivity of any material depends on its temperature and exact chemical composition. This allows, for example, to measure the temperature or humidity of air by measuring its relative permittivity.

Materials with high value of permittivity are used for electrical insulation to prevent the electric field from dissipating around electrical charges.