58.5 million excess electrons are inside a closed surface. What is the net electric flux through the surface?.

Net flux through the surface = (net charge inside) / ε₀

and ε₀ = 8.85 x 10⁻¹² farad/meter.

What's the net charge inside the surface in this problem?

It's (5.85 x 10⁷ electrons) x (the charge on each electron)

= (5.85 x 10⁷ electrons) x (-1.6 x 10⁻¹⁹ coulomb/electron)

= - 9.36 x 10⁻¹² coulomb.

Finally, (net charge inside) / ε₀

= (-9.36 x 10⁻¹² coulomb) / (8.85 x 10⁻¹² farad/meter)

= - 1.058 newton-m²/coulomb.