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 ((D)) at a point in a material when the electric field intensity ((E)) is given, we use the relationship: [D = epsilon E] where (epsilon) is the permittivity of the material and (E) is the electric field intensity.

The permittivity of a material is given by: [epsilon = epsilon_0 epsilon_r] where (epsilon_0) is the permittivity of free space ((8.854 times 10^{-12} , F/m)), and (epsilon_r) is the relative permittivity of the material.

Given that the field intensity (E = 2xyz) and the relative permittivity of the transformer oil ((epsilon_r)) is 2.2, at point P(1,2,3), we substitute (x=1), (y=2), and (z=3) into (E = 2xyz) to find the electric field intensity at this point. Therefore, [E = 2 times 1 times 2 times 3 = 12 , V/m]

Now, find the permittivity of the transformer oil. Using the given (epsilon_r = 2.2), [epsilon = epsilon_0 epsilon_r = 8.854 times 10^{-12}