Magnetic field - General current in a cube

In summary, the magnetic field at the center of the cube may not always be zero, depending on the details of the current density.
  • #1
pieuler
3
2
Homework Statement
Given a cube carrying current, such that the current enters and leaves the cube at any two arbitrary points, prove that the magnetic field at the centre of the cube will always be 0.
Relevant Equations
Biot Savart Law
Ampere Circuit law
I could solve a similar (rather, a specific case of the above) where the current entered through a
corner and left from the corner opposite to it along the body diagonal of the cube. For this specific case, I was able to easily exploit symmetry to deduce the answer (0). However, I cannot think of any suitable technique (eg. symmetry) for the general version.

PS. I have basic knowledge of calculus and vectors, but not so much of 'vector calculus'. Any intuitive guidance/hints/solutions are appreciated.
 
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  • #2
I think we need to know more information about the given current density. Saying that it just enters at one point and exits at another point is not enough. We need to know what is the in between path (is it a straight line? it is some sort of helix? or what else, they can be infinite ways for the inbetween path) and how the current density varies spatially in this path.

If you have some image or figure you can post here please do it, many times one picture worth thousands of words.

I don't think we can prove that the magnetic field at the center will always be zero, regardless of the details of the current density.
 
  • #3
Current is constant and uniform. No specific details about current/current density were given so I believe it's supposed to be constant and uniform(like no variations whatsoever). Current flows along the edges only.

IMG_2890.jpg

Basically, any two completely random points on the edges of the cube. The setup is like a cubical cage made of wires. So that tells you that the current flows only along the edges.
 
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Likes Delta2
  • #4
I still don't see how it would be possible to prove that the magnetic field would be zero at the center, my opinion is that it depends on the entry point, on the exit point and which edges (or parts of edges) are "active" that is they carry the current.
 
  • #5
Delta2 said:
I still don't see how it would be possible to prove that the magnetic field would be zero at the center, my opinion is that it depends on the entry point, on the exit point and which edges (or parts of edges) are "active" that is they carry the current.
How about we consider the edges to be resistances (equal of course) and then think about the current distribution? That is one way of doing the specific case I mentioned, so it might help in the general case too.
 

FAQ: Magnetic field - General current in a cube

1. What is a magnetic field?

A magnetic field is a force field created by moving electric charges, such as electrons. It is represented by lines of force that indicate the direction and strength of the magnetic force at any given point.

2. How is a magnetic field created?

A magnetic field is created by the movement of electric charges, such as the flow of current through a wire or the spin of electrons in an atom. It can also be created by permanent magnets or electromagnets.

3. What is the relationship between magnetic field and current?

Magnetic fields and electric currents are closely related. When an electric current flows through a wire, it creates a magnetic field around the wire. Similarly, a changing magnetic field can induce an electric current in a nearby wire.

4. What is the significance of a magnetic field in a cube?

A magnetic field in a cube can have various applications, such as in magnetic storage devices, motors, generators, and medical imaging machines. It can also help us understand the behavior of electrons and other charged particles in different materials.

5. How is the strength of a magnetic field measured?

The strength of a magnetic field is measured in units of tesla (T) or gauss (G). One tesla is equal to 10,000 gauss. The strength of a magnetic field can be measured using a device called a magnetometer, which can detect the direction and strength of the magnetic field at a specific point.

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