Question

if charge is located at center of spherical volume and electric flux through surface of sphere is Φ what would be flux through surface if radius of sphere were tripled?

Answer 1

Answer:

The flux will be nine times as great.

Explanation:

The electric flux due to a charge Q located in the center of a sphere can be obtained using Gauss's law. Considering a Gaussian surface in the form of a sphere of radius r:

$\Phi_E=\int\limits {Ecos\theta dS} \,$

The electric field (E) is parallel to the surface vector (dS), so $\theta=0$

$\Phi_E=\int\limits{Ecos(0)dS} \,\\\Phi_E=E\int\limits{dS} \,\\\Phi_E=ES\\\Phi_E=E4\pi r^2$

Since the electric flux is proportional to the square of the sphere's radius,  if radius of sphere were tripled, the flux will be nine times as great.