Short Answer 
Gauss’s Law connects electric flux through a closed surface to the enclosed charge, stating that the total flux equals the charge divided by the permittivity of free space. For a spherical Gaussian surface surrounding a point charge, the electric flux remains constant regardless of changes in radius, as the increase in surface area and decrease in electric field strength offset each other, maintaining the relationship ≈í¬∂ = Q.
Step 1: Understand Gauss’s Law
Gauss’s Law is a fundamental principle in physics that relates the electric flux through a closed surface to the enclosed charge within that surface. According to the law, the total electric flux (≈í¬∂) through a closed surface is equal to the charge (Q) inside divided by the permittivity of free space. This establishes a direct correlation between the charge enclosed and the flux, regardless of the size or shape of the surface.
Step 2: Electric Flux and Spherical Surfaces
When dealing with a spherical Gaussian surface and a point charge at its center, the electric flux remains constant regardless of the radius of the sphere. This is due to the fact that the flux (Φ) only depends on the charge (Q) inside the sphere. The formula can be summarized as follows:
- Electric flux (Φ) = Charge (Q)
- Radius change does not affect Φ
Step 3: Effects of Changing the Radius
When the radius of the spherical surface is increased, both the area of the surface and the strength of the electric field change. The area increases by the square of the radius, while the electric field strength decreases by the square of the radius. However, these changes balance out, resulting in:
- No change in the total electric flux through the surface.
- The relationship remains: Φ = Q, independent of radius changes.