Question

If 65.7 milion excess electrons are inside a closed surface What is the net elect=ric flux through the surface? Express your answer in newton meters squared per coulomb.

Answer 1

The net electric flux through a closed surface with 65.7 million excess electrons is -1.188 x 10^3 N·m^2/C, using Gauss's Law.

Step-by-step explanation:

To determine the net electric flux through a closed surface when there are excess electrons, we use Gauss's Law, which states that the net electric flux through any closed surface is equal to the enclosed charge (Q) divided by the permittivity of free space (ε₀), which is 8.85 x 10⁻¹² C²/N·m². In the problem, we are given that there are 65.7 million excess electrons inside a closed surface. One electron has a charge of -1.6 x 10⁻¹⁹ C, so the total excess charge is:

Q = 65.7 x 10⁶ electrons x (-1.6 x 10⁻¹⁹ C/electron) = -1.0512 x 10⁻¹² C

The net electric flux (Φ) through the closed surface is then:

Φ = Q / ε₀ = -1.0512 x 10⁻¹² C / (8.85 x 10⁻¹² C²/N·m²) = -1.188 x 10⁳ N·m²/C

The negative sign indicates that the direction of the electric flux is inward, towards the center of the closed surface. Remember that the net electric flux is a scalar quantity and its direction is not represented in its magnitude.