True or false the net outward flux passing through any closed surfaces equal to the net charge and close by the surface divided by a constant
The correct answer and explanation is:
Correct Answer: True
The statement is true. This concept is directly based on Gauss’s Law, one of Maxwell’s equations in electromagnetism. Gauss’s Law mathematically states that the net electric flux passing through any closed surface is equal to the net electric charge enclosed by the surface divided by a constant. This constant is the electric constant (also called the permittivity of free space), denoted by the symbol ε₀.
Gauss’s Law is expressed in its mathematical form as:
$$
\Phi_E = \frac{Q_{\text{enclosed}}}{\varepsilon_0}
$$
Here,
- $\Phi_E$ is the net electric flux through a closed surface,
- $Q_{\text{enclosed}}$ is the total electric charge enclosed by the surface,
- $\varepsilon_0$ is the vacuum permittivity, a constant approximately equal to $8.854 \times 10^{-12} \, \text{C}^2/\text{N·m}^2$.
Electric flux measures how much the electric field “flows” through a surface. A positive flux indicates that the electric field lines are exiting the surface, while a negative flux means the field lines are entering it.
This principle is useful in calculating electric fields for highly symmetric situations, such as spherical, cylindrical, or planar charge distributions. For example, using a spherical surface around a point charge, one can calculate the electric field without integrating over the field vectors.
It is important to note that the law applies only to the charges inside the surface. Any charges outside the surface do not affect the net electric flux, although they might influence the electric field at specific points on the surface.
Therefore, the statement is accurate: the net outward flux through any closed surface is directly proportional to the net charge enclosed and inversely proportional to the electric constant.