Divergence Theorem

It gives the facility to convert surface integral into its equivalent volume integral.

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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 =ρ_v△V = ρ_v△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