Gauss’s Law

The generalization stated in the previous post lead to the following statement also known as gauss’s Law.
“The electric Flux passing through any closed surface is equal to the total charge enclosed by that surface.”
Gauss one of my second Favourites(first being Fourier without doubt) and one of the greatest mathematician of all time. Though he gave the statement but what is fascinating is his mathematical form of the above statement.

Stay Tuned for Complete Derivation of Gauss’s LAw. Coming Soon.

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GENERALIZATION OF FARADAYS EXPERIMENTS WITH CONCENTRIC SPHERES

The results of Faraday experiments with concentric spheres can be summed up as an experimental law by stating that the electric flux passing through any imaginary sphere placed between two conducting sphere is equal to the charge enclosed within the surface of imaginary sphere. This enclosed charge is distributed either on the surface of the imaginary sphere or is located at a point at the center of the imaginary sphere.
However since 1 C of charge produces 1 C of electric flux, the inner conductor might just well have been a cube or a pot shaped conductor, but still the charge on the outer sphere will be the same. Of Course the flux density would change from its symmetrical distribution to an unknown configuration, but +Q C on any inner conductor will induced a –Q C of charge on surrounding sphere. Going a step further replacing outer sphere with a cylindrical conductor and inner sphere with a pot shaped conductor with charge Q. Producing Flux = Q C the induced charge in the cylindrical conductor will be –Q C. How Fascinating right??
This generalization lead to many developments one of them is discussed later in the next post. All the experiments performed by faraday on electromagnetism is a must read for every engineer. He gave us modern electromagnetics which is used almost in every hardware. I would try to post all his experiments, conclusions and generalization details on the site but self reading is the best reading.

Electric Flux and Electric Flux Density

Faradays experiments showed:

Direct proportionaluty between electric flux and charge on the inner sphere. And fortunately for us the constant of proportionality depended on the units used. And thanks to our standard engineers friendly SI units we got that proportionality constant equal to 1. Giving us a simple uncomplicated equation:
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THE FARADAY EXPERIMENT (overview)

The farady experiment is actually a pretty long one. So as not being in my course and beyond my historical scope. This post only covers essential edited out parts of the experiment that gave us modern definition of electric flux.
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Electric Field Intensity

Consider a fixed charge Q1. Let us move a second charge say test charge Qt around the Q1. We observe that the test charge Qt experiences force everywhere around Q1. It is experiencing a force field. Force on it will be given by coulombs law as: Continue reading

The Coulombs Law

Columbs law state that the force between two small objects seperated in a vaccum by distance much greater that the size of each object is proportional to the product of charges on them and inversely proportional to square of distance between them.

where Q1 and Q2 are positive or negative charge quantity measured in columbs and R is the distance between them measured in meters. Here k is proportionality constant given as:

Again another constant € is called permittivity of free space. Measured in Farad per meter(F/m).

The above quantity is not dimensionless. For coulombs law dimensions are C2/N.m2 . This means Farad has units C2/N.m .This makes are coulombs law as: Continue reading