Which equation represents Gauss's law in integral form?

Which equation represents Gauss's law in integral form?

• A. ∮ E · dA = ε0 Q_enclosed
• B. ∮ E dA = Q_enclosed
• C. ∮ E · dA = ε0 Q_enclosed
• D. ∮ E · dA = Q_enclosed / ε0

Answer: (D)

Gauss's law in integral form says that the total electric flux through any closed surface depends only on the charge enclosed by that surface. The flux is computed by integrating the component of the electric field that is normal to the surface over every little area patch, which is exactly what the dot product E · dA captures. The outward flux through the closed surface equals the enclosed charge divided by ε0, the vacuum permittivity. This ensures the units line up and reflects how the field lines emanate from charges in free space. So, if no charge lies inside, the net flux is zero; if a charge Q is inside, the flux is Q/ε0; for multiple enclosed charges, the flux is the sum of those charges divided by ε0. The division by ε0, not multiplication, is essential for the relationship to hold across all scales and configurations.

Gauss's law in integral form says that the total electric flux through any closed surface depends only on the charge enclosed by that surface. The flux is computed by integrating the component of the electric field that is normal to the surface over every little area patch, which is exactly what the dot product E · dA captures. The outward flux through the closed surface equals the enclosed charge divided by ε0, the vacuum permittivity. This ensures the units line up and reflects how the field lines emanate from charges in free space. So, if no charge lies inside, the net flux is zero; if a charge Q is inside, the flux is Q/ε0; for multiple enclosed charges, the flux is the sum of those charges divided by ε0. The division by ε0, not multiplication, is essential for the relationship to hold across all scales and configurations.