Answer:
Step-by-step explanation:
To find the net electric flux through a closed surface, we need to apply Gauss's law:
Phi_E = Q_enclosed / epsilon_0
where Phi_E is the electric flux, Q_enclosed is the net charge enclosed by the closed surface, and epsilon_0 is the electric constant.
Let's consider a spherical closed surface of radius R enclosing the charges. We can divide the surface into two regions: inside and outside the sphere.
For the charges inside the sphere, the net charge enclosed is:
Q_enclosed = +1.00 nC - 3.00 nC = -2.00 nC
Therefore, the electric flux through the inner surface of the sphere is:
Phi_E_inside = Q_enclosed / epsilon_0 = (-2.00 nC) / epsilon_0
For the charge outside the sphere, the net charge enclosed is:
Q_enclosed = +2.00 nC
Therefore, the electric flux through the outer surface of the sphere is:
Phi_E_outside = Q_enclosed / epsilon_0 = (2.00 nC) / epsilon_0
The net electric flux through the closed surface is the sum of the electric flux through the inner and outer surfaces:
Phi_E_net = Phi_E_inside + Phi_E_outside = (-2.00 nC) / epsilon_0 + (2.00 nC) / epsilon_0
= 0
Therefore, the net electric flux through the closed surface is zero. This means that the total amount of electric field lines entering the surface is equal to the total amount of electric field lines leaving the surface. This result is consistent with Gauss's law, which states that the net electric flux through a closed surface is proportional to the net charge enclosed by the surface. In this case, since the net charge enclosed is zero, the net electric flux is also zero.