Electric Flux through Cubical Surface Enclosing Sphere

[Darkgora]

Homework Statement

A uniform charge density of 700 nC/m3 is distributed throughout a spherical volume of radius 6.00 cm. Consider a cubical Gaussian surface with its center at the center of the sphere.

[reference picture]

What is the electric flux through this cubical surface if its edge length is 16.0 cm?

Homework Equations

(Electric Flux) = Derivative of: E(vector) * dA(vector)

(Permittivity Constant) * (Electric Flux) = (Charge Enclosed)

Electric Field of a Sphere = (kq/R^3)r

The Attempt at a Solution

I tried to find to treat the enclosed sphere as a point charge within the Gaussian cube but am unsure about how to calculate the flux within the cube using this quantity.

To find q-enclosed of the sphere i divided its charge density by its volume.

 

[andrewkirk]

Since the cube fully contains the charge, you can just use Gauss's Law. There is no need for any calculus. Just work out the total charge based on the volume of the sphere, then plug that into Gauss's law to find the flux through any closed surface that contains the sphere and no other charges.

 

[Darkgora]

Since the cube fully contains the charge, you can just use Gauss's Law. There is no need for any calculus. Just work out the total charge based on the volume of the sphere, then plug that into Gauss's law to find the flux through any closed surface that contains the sphere and no other charges.

Simple. Thanks!