If a charge is located at the center of a spherical volume...

If a charge is located at the center of a spherical volume and the electric flux through the surface of the sphere is $\Phi$, what would be the flux through the surface if the radius of the sphere were tripled?
A. $3 \Phi$
B. $9 \Phi$
C. $\Phi$
D. $\Phi / 3$
E. $\Phi / 9$

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Key Concepts

Gauss's Law

Gauss's Law states that the total electric flux through a closed surface is directly proportional to the enclosed electric charge. This key concept allows one to calculate flux without relying on the specific geometry of the enclosing surface, as long as the charge remains inside, making it particularly useful in symmetric situations.

Electric Flux

Electric flux measures the number of electric field lines crossing a surface and is used to quantify the strength and direction of an electric field over an area. In contexts involving changes in the size of the surface but constant enclosed charge, electric flux remains unchanged, reflecting its dependence solely on the net charge as per Gauss's Law.

Spherical Symmetry

Spherical symmetry occurs when a system looks the same in every direction from a central point. In problems involving a charge placed at the center of a sphere, this symmetry simplifies the analysis since the electric field has the same magnitude at every point on the sphere. Thus, increasing the radius of the sphere does not alter the total flux, since flux is determined solely by the enclosed charge.

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