Given:
Charge(Q) = 17.7 μC = 17.7 x 10^-6 C
Side of cube(a) = 0.03 m

To find:
Electric flux through each face of the cube.

Explanation:
Electric flux is the measure of the flow of electric field through a surface. It is denoted by the symbol Ф.

Electric flux formula:
Ф = E * A * cosθ
where,
E = Electric field
A = Area of the surface
θ = Angle between electric field and the normal to the surface.

In this problem, the charge is located at the centre of the cube. The electric field is radial and symmetric about the centre of the cube. Hence, the electric field is perpendicular to each of the faces of the cube.

Electric field due to a point charge formula:
E = (1/4πε0) * (Q/r^2)
where,
ε0 = Permittivity of free space = 8.85 x 10^-12 F/m
Q = Charge on the point charge
r = Distance from the point charge to the point where electric field is to be calculated.

In this problem, the distance from the charge to any face of the cube is half of the side length of the cube. Hence,
r = a/2 = 0.015 m

Electric field due to the point charge at the centre of the cube:
E = (1/4πε0) * (Q/r^2)
E = (1/4π8.85 x 10^-12) * (17.7 x 10^-6 / 0.015^2)
E = 1.43 x 10^6 N/C

The electric field is the same for each face of the cube as the electric field is perpendicular to each face.

Electric flux through each face of the cube:
Ф = E * A
As the electric field is perpendicular to each face, the angle between the electric field and the normal to the surface is 0°. Hence, cosθ = 1.

Ф = E * A * cosθ
Ф = E * A * 1
Ф = E * A

Electric flux through each face of the cube:
Ф = E * A
Ф = (1.43 x 10^6) * (0.03^2)
Ф = 386.37 Nm^2/C

Hence, the electric flux through each face of the cube is 386.37 Nm^2/C.

Answer: Electric flux through each face of the cube is 386.37 Nm^2/C.