Physics flux question plz help?

Question

Three charges (+Q1, +Q2 and +Q3) are located within a sphere made of

dielectric material with relative permittivity ε1. Two other charges, +Q4

and –Q5, are located outside this sphere, which is surrounded by a

dielectric medium with relative permittivity ε2.

(i) What is a total electric flux through the surface of the sphere?

(ii) Which of the charges contribute to the field at a given point on

the surface of the sphere?

(iii) Write the general vector equation which relates electric field and

electric flux density.

I have tried to solve it, i knw the formula for E-flux

=> ψ = Intgr( D.dS)

Answer 1

(i) According to Gaus's law, the total electric flux through a surface equals

Q/(ε0 * εr),

where ε0 = permittivity of free space

εr = relative permittivity of the material inside the surface.

Q = total charge in the volume enclosed by the surface.

In the given problem εr = ε1

Charges Q4 and Q5 are outside the volume. So, they are not to be considered.

Total charge inside the volume Q = Q1 + Q2 + Q3

Therefore, electric flux = (Q1 + Q2 + Q3)/(ε0 * ε1)

(ii) All the five charges contribute to the field. But only Q1, Q2, Q3 contribute to the flux.

(iii) The relation between electric field and flux is

integral E.dS = electric flux

where E = electric field vector

dS = a vector whose magnitude is the area of an infinitesimal part of the surface and whose direction is perpendicular to and pointing outward this part.

. represents dot product