Electric Flux Density is independent of material properties: Justify/Contradict.In the region of free space that includes the volume 2 < x,y,z < 3.D = [ (2y/z)ax + (2x/z)ay - (4xy/z2)az) ] C/m2(i) Evaluate the volume integral side of the divergence theorem for the volumedefined by 2 < x,y,z < 3

Electric Flux Density, also known as electric displacement, is a vector field that describes the flow of electric flux through a given area. It is represented by the symbol D and is measured in coulombs per square meter (C/m^2).

The given expression for D in the region of free space is D = [(2y/z)ax + (2x/z)ay - (4xy/z^2)az]. This expression represents the electric flux density at any point in the region.

To evaluate the volume integral side of the divergence theorem for the volume defined by 2 < x, y, z < 3, we need to calculate the divergence of D and integrate it over the volume.

The divergence of D, denoted as ∇ · D, can be found by taking the dot product of the gradient operator (∇) with D. In this case, the gradient operator is given by ∇ = (∂/∂x)ax + (∂/∂y)ay + (∂/∂z)az.

Taking the dot product, we have ∇ · D = (∂/∂x)(2y/z) + (∂/∂y)(2x/z) + (∂/∂z)(-4xy/z^2).

To evaluate the volume integral, we integrate the divergence of D over the given volume. Since the volume is defined by 2 < x, y, z < 3, the integral becomes:

∫∫∫ (∇ · D) dV = ∫∫∫ [(∂/∂x)(2y/z) + (∂/∂y)(2x/z) + (∂/∂z)(-4xy/z^2)] dV

where dV represents the differential volume element.

To solve this integral, we need to perform the partial derivatives and integrate over the volume. However, since the expression for D is not provided, we cannot proceed with the calculation.