Line of infinite charge and a gaussian sphere

In summary, constructing a spherical gaussian surface centered on an infinite line of charge allows us to calculate the flux through the sphere and prove that it satisfies Gauss' Law. While it may seem tedious, integrating over a hemispherical surface and multiplying by two shows the power of symmetry in applying the law. By finding E(r) at a point with polar angle \theta and integrating over the entire sphere, the calculation is not difficult.
  • #1
stunner5000pt
1,461
2
Construct a spherical gaussian surface centered on an infinite line of charge. Calculate the flux through the sphere and thereby show that it satisfies gauss law.

I know how i can do it for a cylinder, but a sphere?

I know that the ends of the wire (one diameter) wil have zero flux at it's ends

but wouldn't i have to integrate over a big hemispherical surface and then multiply by two but ... wouldn't it be tedious?
 
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  • #2
stunner5000pt said:
but wouldn't i have to integrate over a big hemispherical surface and then multiply by two but ... wouldn't it be tedious?

Yes, but that's probably the reason they're asking you to do it. It shows the power of symmetry in applying Gauss' Law.
 
  • #3
It's not hard. You know what E(r) is. Take a point at polar angle \theta and find E(r).n in terms of \theta. Integrate over the sphere.
 

1. What is a line of infinite charge and a gaussian sphere?

A line of infinite charge is a theoretical construct in electrostatics where a line is assumed to have an infinite amount of charge distributed along its length. A gaussian sphere is a hypothetical spherical surface surrounding the line of charge, used to calculate the electric field and potential at any point in space.

2. What is the significance of studying a line of infinite charge and a gaussian sphere?

Studying a line of infinite charge and a gaussian sphere allows us to understand the behavior of electric fields and potentials in a simplified yet mathematically tractable scenario. This can help us understand more complex systems and also has practical applications in physics and engineering.

3. How is the electric field and potential calculated for a line of infinite charge and a gaussian sphere?

The electric field and potential are calculated using Gauss's Law, which states that the net electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space. For a line of infinite charge, the electric field is inversely proportional to the distance from the line, and for a gaussian sphere, the electric field and potential follow a similar behavior to that of a point charge.

4. How does the electric field and potential change with distance from the line of infinite charge?

As the distance from the line of infinite charge increases, the electric field and potential decrease. This is because the electric field and potential are inversely proportional to the distance from the line, following an inverse-square law. The electric field and potential also vary with the angle from the line, with the strongest values being perpendicular to the line.

5. Are there any real-world applications of a line of infinite charge and a gaussian sphere?

Although an infinite line of charge and a gaussian sphere do not exist in the real world, the concept is used to model and understand the behavior of electric fields and potentials in various systems, such as parallel plate capacitors and charged particle beams. It is also used in theoretical studies of electrostatics and has practical applications in fields such as telecommunications and electronics.

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