Find the electric flux density surrounding a material with field intensity of 2xyz placed in transformer oil ( εr = 2.2) at the point P(1,2,3) is (in 10-10 units)

To find the electric flux density surrounding a material with a given electric field intensity in transformer oil, we first need to understand the relationship between electric flux density ((mathbf{D})), electric field intensity ((mathbf{E})), and the permittivity of the medium ((epsilon)). The relationship can be expressed as:

[mathbf{D} = epsilon mathbf{E}]

where (epsilon = epsilon_0 epsilon_r), (epsilon_0) is the permittivity of free space ((8.85 times 10^{-12} F/m)), and (epsilon_r) is the relative permittivity of the medium (for transformer oil, (epsilon_r = 2.2)).

Given:

– Electric field intensity, (mathbf{E} = 2xyz) (where (x), (y), and (z) are the coordinates in meters),

– Relative permittivity of transformer oil, (epsilon_r = 2.2),

– Point (P(1,2,3)).

First, calculate (epsilon):

[epsilon = epsilon_0 epsilon_r = (8.85 times 10^{-12} F/m) times 2.2]

[epsilon = 1.947 times 10^{-11} F/m]

Next, calculate the electric field