Question

The three small spheres shown in the figure below carry charges q₁ = 3.05 nC, q₂ = -8.20 nC, and q₃ = 2.90 nC.

Answer 1

Hi

for starters let's define "gauss's law" which is the law that governs this type of phenomena

$\Phi = \frac {q_{1}}{\epsilon_{o}}$

where "q" is the enclosed charge on the surface and "epsilon" it is the constant of permittivity   $\epsilon_{o}= 8.85*10^{-12}$

so

Surface 1   

$\Phi_{1} = \frac {q_{1}}{\epsilon_{o}}=\frac {3.05 *10^{-9}C}{8.85*10^{-12}}=344.632 N*m^{2}/C$

Surface 2

$\Phi_{2} = \frac {q_{2}}{\epsilon_{o}}=\frac {-8.20 *10^{-9}C}{8.85*10^{-12}}=-926.553 N*m^{2}/C$

Surface 3

$\Phi_{3} = \frac {q_{1}+q_{2}}{\epsilon_{o}}=\frac {(3.05-8.20) *10^{-9}C}{8.85*10^{-12}}=-581.920 N*m^{2}/C$

Surface 4

$\Phi_{4} = \frac {q_{1}+q_{3}}{\epsilon_{o}}=\frac {(3.05+2.90) *10^{-9}C}{8.85*10^{-12}}=672.316 N*m^{2}/C$

Surface 5

$\Phi_{5} = \frac {q_{1}+q_{2}+q_{3}}{\epsilon_{o}}=\frac {(3.05-8.20+2.90) *10^{-9}C}{8.85*10^{-12}}=-254.237 N*m^{2}/C$

I hope I have responded and have been helpful. Any questions you have please feel free to comment

Cheers