Electric Flux through Cubical Surface Enclosing Sphere

In summary, the problem involves a uniform charge density of 700 nC/m3 distributed throughout a spherical volume of radius 6.00 cm. The question is asking for the electric flux through a cubical Gaussian surface with its edge length at 16.0 cm. Using Gauss's Law, the total charge based on the volume of the sphere can be calculated and plugged into the law to find the flux through any closed surface that contains the sphere and no other charges. There is no need for calculus in this problem.
  • #1
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.
phy 3.png
 
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  • #2
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.
 
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Likes Darkgora
  • #3
andrewkirk said:
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!
 

Related to Electric Flux through Cubical Surface Enclosing Sphere

What is electric flux?

Electric flux is a measure of the amount of electric field passing through a given surface. It is calculated by taking the dot product of the electric field vector and the surface area vector.

How is electric flux through a surface calculated?

The electric flux through a surface is calculated by taking the integral of the dot product of the electric field and the surface area vector over the surface. In simpler terms, it is the sum of the electric field passing through each small portion of the surface.

What is a cubical surface enclosing a sphere?

A cubical surface enclosing a sphere is a cube-shaped surface that completely surrounds a sphere. It is often used in physics problems to simplify the calculation of electric flux.

How does the electric flux through a cubical surface enclosing a sphere differ from other shapes?

The electric flux through a cubical surface enclosing a sphere is the same as the electric flux through any other shape enclosing the same sphere. This is because the flux depends on the electric field and the surface area, which are both the same for any shape enclosing the same sphere.

What is the significance of calculating electric flux through a cubical surface enclosing a sphere?

Calculating electric flux through a cubical surface enclosing a sphere can help in understanding the behavior of electric fields and their relationship to different shapes. It is also a useful tool in solving practical problems involving electric fields and charges.

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