E&M : Simulate/Calculate B field due to J

In summary, the conversation discusses the need to calculate the magnetic field inside and around a square conductor with non-uniform conductivity. The problem can be solved through numerical simulation using software such as Mathematica or Ansys. The frequency range and physical sizes are not specified, but the field must be calculated accurately at all ranges. The possibility of using Biot-Savart Law or writing a custom code is also mentioned.
  • #1
Hepth
Gold Member
464
40
My end goal is to analytically or numerically calculate the magnetic field inside and around a square conductor that has connection points at the top and bottom with a voltage applied.

Are there any software packages (mathematica, or even just C) that can do this given ANY current density in the conductor? The problem is that the conducting square does not have uniform conductivity, and can, in theory, have gradients, dead spots, etc, thus creating some eddy currents or some asymmetry that I cannot calculate easily by hand, hence numerical simulation would be perfect.

An example would be : a square conductor with leads at top and bottom. Some voltage is applied. The square conductor is split in two where the left side is rho_1 resistivity and right side is rho_2.

This specific one I think I can numerically do IF the leads connected the entire top, then its just integrate contributions from a number of line segments and you're done. But if the geometry of conductance is not simple I get stuck.

tldr: Any good simulation/numerical calculation for B fields given a specific current density equation.
 
Physics news on Phys.org
  • #2
Most people I know with this problem use Ansys. It's commercial, and I understand not cheap.
 
  • #3
What frequency range and physical sizes are we talking about here?
 
  • #4
Do you need the field close to the conductor? Farther away, the details of the current density are irrelevent.
 
  • #5
Yes, I need all ranges with no approximation, including fields in parts of the conductor due to currents in other parts. No frequency range, can be a static current, about an amp, resistance varies, physical dimensions should be irrelevant as processes should scale.
 
  • #6
Hepth said:
physical dimensions should be irrelevant as processes should scale.
Your statement isn't clear. This is a static current? Because if it's AC, eddy currents are scale dependent.
 
  • #7
If it's AC, you might want to look into NEC (Numerical Electromagnetics Code) which is a wire MOM code. If it's just static currents then... well you could always write your own code to deal with it. A lot of books that deal with electromagnetics and method of moments will discuss some kind of static case though usually it's in terms of charge via the Poisson equation. But I also think you could easily just use the Biot-Savar Law. You can get an approximation of the current by finding the equivalent resistance of each section of the wire and treating it like a circuit problem and then using the solved currents as uniform currents over the surface of the conductor. Then you can integrate over the currents as given by Biot-Savart for an infinitesimal current element.
 

1. What is E&M and how does it relate to calculating B field?

E&M stands for electromagnetism, which is the study of the relationship between electricity and magnetism. In order to calculate the B field, which represents the magnetic field, one must use the principles of E&M to understand the behavior of charged particles and their interactions with magnetic fields.

2. What is the importance of simulating B field due to J?

Simulating B field due to J allows scientists to understand and predict the behavior of charged particles in electromagnetic fields. This is crucial in various fields such as engineering, astrophysics, and materials science.

3. How is the B field due to J calculated?

The B field due to J is calculated using the Biot-Savart law, which states that the magnetic field at a point is directly proportional to the current passing through a wire and inversely proportional to the distance from the wire. This law can be applied to calculate the B field at any given point due to a current-carrying wire.

4. What factors can affect the B field due to J?

The strength of the B field due to J is affected by several factors, including the magnitude and direction of the current, the distance from the current-carrying wire, and the permeability of the medium in which the wire is located. Additionally, the shape and orientation of the wire can also impact the B field.

5. Can the B field due to J be visually represented?

Yes, the B field due to J can be visually represented using vector arrows, where the length and direction of the arrows indicate the strength and direction of the magnetic field. This can help in understanding the behavior of charged particles in the presence of a current-carrying wire.

Similar threads

  • Classical Physics
Replies
9
Views
1K
  • Electromagnetism
Replies
2
Views
1K
  • Electromagnetism
Replies
7
Views
890
  • Electromagnetism
Replies
4
Views
852
Replies
2
Views
714
  • Introductory Physics Homework Help
Replies
26
Views
474
Replies
4
Views
1K
Replies
0
Views
229
  • Introductory Physics Homework Help
2
Replies
40
Views
765
Replies
4
Views
906
Back
Top