Calculating Flux Through a Gaussian Spherical Shell Inside a Charged Sphere

In summary, a positive charge is uniformly distributed throughout the volume of an insulating sphere with radius R. The volume charge density is represented by ρ. The problem asks for the flux through a Gaussian spherical shell with a radius of R/2, which is contained inside the charged sphere and centered at a distance of R/2 from the center of the charged sphere. The formula for flux is qenclosed/Eo. The solution involves taking ρ times the volume enclosed (4/3)*∏*(r/2)^3 and dividing it by Eo to get the correct result.
  • #1
Gee Wiz
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Homework Statement


An insulating sphere of radius R has positive charge uniformly distributed throughout its volume. The volume charge density (i.e., the charge per volume) is ρ.

What is the flux through a Gaussian spherical shell of radius R/2 that is totally contained inside the charged sphere and centered a distance R/2 from the center of the charged sphere, as shown by the dashed sphere in the diagram below?

Homework Equations


flux=(qenclosed/Eo)

The Attempt at a Solution


I initially took ρ times the volume enclosed (4/3)*∏*(r/2)^3 and then divided that by Eo. But it didn't give me the correct result
 
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  • #2
nevermind. figured it out
 

What is "Flux through Gaussian sphere"?

Flux through Gaussian sphere is a concept in electromagnetism that represents the amount of electric or magnetic field passing through a closed surface. It is calculated using the Gauss's law, which states that the total flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space.

How do you calculate the "Flux through Gaussian sphere"?

The flux through a Gaussian sphere can be calculated by taking the dot product of the electric or magnetic field vector with the normal vector to the surface. This product is then multiplied by the surface area of the sphere and the cosine of the angle between the two vectors.

What is the significance of "Flux through Gaussian sphere"?

Flux through Gaussian sphere is important in understanding the behavior of electric and magnetic fields. It helps in determining the strength and direction of the field at a particular point, as well as the total amount of field passing through a given surface. It also plays a crucial role in the applications of electromagnetism, such as in electrical engineering and telecommunications.

What factors affect the "Flux through Gaussian sphere"?

The flux through a Gaussian sphere is affected by the strength and direction of the electric or magnetic field, the surface area of the sphere, and the angle between the field vector and the normal vector to the surface. It is also influenced by the permittivity of free space and the charge enclosed by the sphere.

Can "Flux through Gaussian sphere" be negative?

Yes, the flux through a Gaussian sphere can be negative if the field vector and the normal vector to the surface are in opposite directions. This indicates that the field is leaving the closed surface rather than entering it. A negative flux value does not necessarily mean a weaker field, as it depends on the strength of the field and the surface area of the sphere.

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