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.
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.
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: