The three small spheres as shown in figure carry charges `q_1 = 4nC, q_2 = -7.8nC and q_3 = 2.4nC`. Find the net electic flux through each of the following closed surfaces shown in cross section in the figure.
a. `S_1` b.`S_2`
c. `S_3` d. `S_4`
e. `S_5`.
Do your answers to parts from (a) to (e) depend on how the charge is distributed over each small sphere? Why or why not?
.

Explanation

a. `Phi_(S_1) = q_1//epsilon_0 = (4.00 xx 10^(-9)C)//epsilon_0 = 452 Nm^2//C`
b. `Phi_(S_2) = q_2//epsilon_0 = (-7.80 xx 10^(-9)C)//epsilon_0 = -881Nm^2//C`
c. `Phi_(S_3) = (q_1 + q_3)//epsilon_0 = ((4.00 - 7.80) xx 10^(-9)C)//epsilon_0`
`= -429 Nm^2//C`
d. `Phi_(S_4) = (q_1 +q_3)//epsilon_0 = ((4.00 + 2.40) xx 10^(-9)C)//epsilon_0`
`= 723Nm^2//C`
e. `Phi_(S_5) = (q_1+q_2+q_3)/epsilon_0 = ((4.00 - 7.80 + 2.40) xx 10^(-9)C)/epsilon_0`
` = - 158 Nm^2//C`
All that matters for Gauss's law is the total
amount of charge enclosed by the surface, not its
distribution within the surface.