Electric field calculations for a spherical grid

In summary, the document discusses methods for calculating electric fields generated by charges arranged in a spherical grid configuration. It outlines the mathematical principles involved, including the use of Gauss's law and the superposition principle, to determine the resultant electric field at various points in space. The analysis emphasizes the symmetry of the spherical grid, which simplifies the calculations and allows for efficient computational techniques. The findings are applicable in fields such as electrostatics and electromagnetic theory.
  • #1
Jz21
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TL;DR Summary
I need help calculating the radius required to achieve a electric field strength of 1 x 10/6 v/m on a spherical grid inside a vacuum chamber
Hello, I need some help regarding how to calculate the needed radius to achieve 1 x 10/6 v/m on the surface of a spherical inner grid, inside a conductive vacuum chamber. I have used various equations, however I don’t know if they are very good and would like to know other methods. Thanks!
 
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  • #2
Welcome to PF.

Jz21 said:
TL;DR Summary: I need help calculating the radius required to achieve a electric field strength of 1 x 10/6 v/m on a spherical grid inside a vacuum chamber

Hello, I need some help regarding how to calculate the needed radius to achieve 1 x 10/6 v/m on the surface of a spherical inner grid, inside a conductive vacuum chamber. I have used various equations, however I don’t know if they are very good and would like to know other methods. Thanks!
Woo-wee. 1MeV/m -- whatcha' tryn' to do?
 
  • #3
A lil bit of amateur fusion, that’s all
 
  • #4
Jz21 said:
Hello, I need some help regarding how to calculate the needed radius to achieve 1 x 10/6 v/m on the surface of a spherical inner grid, inside a conductive vacuum chamber.
If the walls of the chamber are smooth, without projections, then knowing the voltage, you must place a sphere in the chamber that has a maximum diameter consistent with that voltage gradient.

What is your working voltage?
What is the radius of the vacuum chamber?
 
  • #5
Just a lil bit of fusion, nothing else
 
  • #6
Jz21 said:
spherical inner grid
If you mean a wire mesh. I can tell you right now that this isn't going to work.

The field near the wire will be driven by the radius of the wire, not the radius of the sphere. That will be maybe two orders of magnitude greater, and the wire will not survive.
 
  • #7
Sorry, I didn’t thought I didn’t reply to the other reply, my bad. I am working with 40 kv dc, and the radius of the chamber is 5 inches. There are also no projections, with only a feed through stalk.
 
  • #8
Vanadium 50 said:
If you mean a wire mesh. I can tell you right now that this isn't going to work.

The field near the wire will be driven by the radius of the wire, not the radius of the sphere. That will be maybe two orders of magnitude greater, and the wire will not survive.
It is not wire mesh, but just standard wire loops.
 
  • #9
Vanadium 50 said:
If you mean a wire mesh. I can tell you right now that this isn't going to work.

The field near the wire will be driven by the radius of the wire, not the radius of the sphere. That will be maybe two orders of magnitude greater, and the wire will not survive.
Oh ok I see what you mean.
 
  • #10
Jz21 said:
I am working with 40 kv dc, and the radius of the chamber is 5 inches.
40 kV, radius = 5".
5" = 0.125 metre.

1 MV/m is 1 kV/mm, so there needs to be a gap of 40 mm between the chamber wall and the sphere.
The sphere radius will be (125 mm - 40 mm) = 85 mm, or 170 mm diameter = 6.75" diameter. It will need to have a smooth surface.

The support stalk for the sphere will need to be carefully constructed to prevent voltage breakdown along its surface.
 
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  • #11
Baluncore said:
40 kV, radius = 5".
5" = 0.125 metre.

1 MV/m is 1 kV/mm, so there needs to be a gap of 40 mm between the chamber wall and the sphere.
The sphere radius will be (125 mm - 40 mm) = 85 mm, or 170 mm diameter = 6.75" diameter. It will need to have a smooth surface.

The support stalk for the sphere will need to be carefully constructed to prevent voltage breakdown along its surface.
Thank you. But I now realize I was going about it all wrong. I was approximating the grid as a sphere as it forms a sphere, but is still made of wire. So now I know we’re to go.
 

FAQ: Electric field calculations for a spherical grid

What is an electric field and how is it calculated for a spherical grid?

An electric field is a vector field around charged particles that exerts a force on other charged particles. To calculate the electric field for a spherical grid, one typically uses Coulomb's law, which states that the electric field (E) due to a point charge (Q) at a distance (r) is given by E = k * Q / r², where k is Coulomb's constant. For a spherical grid, the total electric field is determined by summing the contributions from all point charges distributed over the surface of the sphere.

What are the key variables involved in electric field calculations for a spherical grid?

The key variables include the charge magnitude (Q), the distance from the charge to the point of interest (r), the permittivity of free space (ε₀), and the number of charges distributed over the spherical surface. Additionally, the angles (θ, φ) in spherical coordinates may be relevant for calculating the direction of the electric field vector.

How does the symmetry of a spherical grid affect electric field calculations?

The symmetry of a spherical grid simplifies electric field calculations significantly. Due to the uniform distribution of charge over the surface, the electric field at points along the axis of symmetry can often be determined without integrating over the entire surface. This allows for the use of Gauss's law, which states that the electric field can be calculated based on the enclosed charge and the geometry of the surface.

What are the common methods used for numerical calculations of electric fields in spherical grids?

Common methods for numerical calculations include the Finite Element Method (FEM), the Finite Difference Method (FDM), and the Boundary Element Method (BEM). These methods discretize the spherical grid into smaller elements or nodes, allowing for the approximation of the electric field by solving the governing equations numerically. Software tools like COMSOL Multiphysics or MATLAB can be utilized to perform these calculations efficiently.

What are the applications of electric field calculations in spherical grids?

Electric field calculations in spherical grids have numerous applications, including in electrostatics, capacitor design, and modeling of charged particle interactions in fields such as astrophysics and plasma physics. They are also relevant in designing devices such as sensors, antennas, and medical imaging equipment, where understanding the electric field distribution is crucial for performance optimization.

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