What does Gauss's law state about total electric flux?

What does Gauss's law state about total electric flux?

• A. It is unaffected by charges outside the surface
• B. It is always constant
• C. It equals the total charge within the closed surface
• D. It varies with distance from the surface

Answer: (C)

Gauss's law is a fundamental principle in electrostatics that relates the electric flux through a closed surface to the charge enclosed by that surface. Specifically, it states that the total electric flux through a closed surface is directly proportional to the total charge enclosed within that surface. This relationship can be mathematically expressed using the equation: Φ_E = Q_enc / ε_0 Here, Φ_E represents the electric flux, Q_enc is the total charge enclosed within the closed surface, and ε_0 is the permittivity of free space. The implication of this law is that only the charge contained within the boundary of the closed surface contributes to the electric flux. Any charges located outside the closed surface do not influence the total electric flux through it. This makes Gauss's law especially useful in simplifying the analysis of electric fields, particularly in situations with symmetrical charge distributions, where calculating the electric field directly can be cumbersome. The correctness of the answer is rooted in the intrinsic nature of electric fields and their relationship to charge as described by Gauss's law.

Gauss's law is a fundamental principle in electrostatics that relates the electric flux through a closed surface to the charge enclosed by that surface. Specifically, it states that the total electric flux through a closed surface is directly proportional to the total charge enclosed within that surface. This relationship can be mathematically expressed using the equation:

Φ_E = Q_enc / ε_0

Here, Φ_E represents the electric flux, Q_enc is the total charge enclosed within the closed surface, and ε_0 is the permittivity of free space.

The implication of this law is that only the charge contained within the boundary of the closed surface contributes to the electric flux. Any charges located outside the closed surface do not influence the total electric flux through it. This makes Gauss's law especially useful in simplifying the analysis of electric fields, particularly in situations with symmetrical charge distributions, where calculating the electric field directly can be cumbersome.

The correctness of the answer is rooted in the intrinsic nature of electric fields and their relationship to charge as described by Gauss's law.