It gives the facility to convert surface integral into its equivalent volume integral.
Statement:- It states that the surface integral of a normal component of any vector function on a closed surface is equal to the volume integral of the divergence of vector function.
Proof:- The total charge enclosed by volume △V is given by
........(3)
........(4)
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Statement:- It states that the surface integral of a normal component of any vector function on a closed surface is equal to the volume integral of the divergence of vector function.
Proof:- The total charge enclosed by volume △V is given by
........(1)
The total outward flux coming out from the volume is △V equal to the charge enclosed.
△Ψ = △Q = charge density x volume
△Ψ = △Q =ρv△V = ρv△x△y△z.......(2)
From equation (1) and (2)........(3)
The divergence of D is given by
........(4)
From (3) and (4)
According to Gauss's Law
ψ = Q
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