divergence theorem & maxwell’s first equation

Name :- Smit Shah -140410109096

S.Y electrical 2 Sem 4

Subject:-FT

Topic :- Divergence Theorem &Maxwell’s First Equation..

Divergence of a vectorThe divergence of vector field A at a point is

the net outward flux of A per unit volume as the volume about the point to zero.

Integral form of divergenceIt state that the volume integral of the vector

field A is equal to the surface integral of a taken over enclosing surface.

The expression for div D in three co-ordinate system..Cartesian coordinates

Cylindrical coordinates

Spherical coordinates

Maxwell’s First Equation

Maxwell’s first equation is based on Gauss’ law of electrostatics published in 1832, wherein Gauss established the relationship between static electric charges and their accompanying static fields.

Gauss law..The total electric flux crossing the closed

surface is equal to the total charge enclosed by that path..

The above integral equation states that the electric flux through a closed surface area is equal to the total charge enclosed.

The differential form of the equation states that the divergence or outward flow of electric flux from a point is equal to the volume charge density at that point.

Divergence of D due to some simple charge Configuration…

(A) Divergence of D due to point charge..

(B) Divergence of D due to Uniform Line Charge..

Consider a uniform line charge with density is placed along z- axis. The flux density D due to this charge at a distance p from line charge is..