What is the total flux flowing through a spherical Gaussian surface?

In summary, the question asks about the total flux through a spherical Gaussian surface with radius R/2 concentric to a uniformly charged sphere of radius R. The solution involves using Gauss' Law and the equations for volume and surface area of a sphere to calculate the flux as Q/8ε0. The correctness of this solution is confirmed and further explanation is requested.
  • #1
CM Longhorns
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Homework Statement


Consider a uniformly charged sphere (an insulating sphere of radius R,) and a spherical Gaussian surface with radius R/2 concentric to the sphere. What is the total flux flowing through the Gaussian surface?

Homework Equations


Vsphere= (4∏R^3)/3
Asphere= 4∏R^2

Gauss' Law:
Flux = ρVinside/ε0 = PHI = QVinside/Voutside

The Attempt at a Solution


Ok, so I am familiarizing myself with these concepts, and I can't find a concrete example such as this one in the text. I'm pretty sure that simply by relating the equations for volume by Gauss' Law above can give me a compact expression for the Flux. BUT I'm not sure.
I gave it a shot by using the eqn above and simplified this expression to Q/8ε0. I am skeptical of its correctness. Can someone explain if I'm doing this correctly, and if so qualitatively describe why? Thanks! First post!
 
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  • #2
Resolved.
 

FAQ: What is the total flux flowing through a spherical Gaussian surface?

1. What is a spherical Gaussian surface?

A spherical Gaussian surface is a hypothetical surface that is used to calculate the total flux, or flow of a vector field, through a closed surface. It is a perfectly spherical shape that is used as a simplified model for calculating flux.

2. How is the total flux calculated through a spherical Gaussian surface?

The total flux through a spherical Gaussian surface is calculated by taking the dot product of the vector field and the normal vector at each point on the surface, and then integrating these dot products over the entire surface. This calculation takes into account the direction and magnitude of the vector field at each point on the surface.

3. Can the total flux through a spherical Gaussian surface be negative?

Yes, the total flux through a spherical Gaussian surface can be negative. This occurs when the vector field is oriented in the opposite direction of the normal vector at a specific point on the surface. This means that the vector field is flowing out of the surface instead of into it, resulting in a negative flux value.

4. What is the unit of measurement for total flux through a spherical Gaussian surface?

The unit of measurement for total flux through a spherical Gaussian surface is determined by the unit of measurement for the vector field. For example, if the vector field represents fluid flow, the unit of measurement would be volume per unit time. If the vector field represents an electric field, the unit of measurement would be electric flux per unit area.

5. What is the significance of calculating total flux through a spherical Gaussian surface?

Calculating the total flux through a spherical Gaussian surface is significant because it allows us to understand and quantify the flow of a vector field through a closed surface. This can be useful in various scientific applications, such as calculating the amount of fluid passing through a pipe or the amount of electric charge passing through a closed surface.

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