what is gauss theorem
Answers
heya...
The Gaussian curvature (the product of the principal curvatures) of a regular surface in Euclidean space remains unchanged when the surface is isometrically deformed. Gauss' theorem follows from the fact that the Gaussian curvature of a surface at a point can be expressed in terms of the coefficients of the first fundamental form of the surface,
and their first and second derivatives at that point. Such an expression for is called the Gauss equation, which may be written down in several forms [2]. The Gauss equation simplifies in special coordinates. Thus, in isothermal coordinates (, )
The Gauss equation and the Peterson–Codazzi equations form the conditions for the integrability of the system to which the problem of the reconstruction of a surface from its first and second fundamental forms may be reduced. It follows from Gauss' theorem and from the Gauss–Bonnet theorem that the difference between the sum of the angles of a geodesic triangle on a regular surface and is equal to the oriented area of the spherical image of this triangle [1].
Explanation:
To understand this theorem before , you must know about the few terms as follow :
1) Electric flux
2) Surface Area
3) Electric field
Electric field is a characteristics of a space when a charge particle enters the field , it starts accelerating.
It is vector quantity , its direction shown accordingly by the nature of electric charge...
As we know that flowing water is a vector quantity as it has some velocity and direction but when yhe same water stores somewhere it occupy some space and become volume of water...This volume of water here is a scalar quantity...
The same concept we use here as we know that Electeic field is a vector quantity but if we count the field lines linked to the surface area , it become just a number i.e, scalar...
Electeic flux is define as the number of filed lines linked to the surface area...
Gauss is the one find out how to find out or measure this electeic flux...
According to Gauss , The electric flux linked to the surface area is equal to charge q times 1 /€ .
where q = net charge , € = permitivity of free space
The above one is Gauss theorem...
lack of greek alphabets and symbols ...cant write proper relation and formula here...so refer booj for the relation of electric flux...
Hope this help...