A solved problem from Griffiths creats problem

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In summary, the conversation discusses a solved problem from Griffiths that creates a new problem. The problem requires finding the vector potential of an infinite solenoid with n turns per unit length, radius R, and current I. Griffiths relates the integral form of Ampere's law to [closed integral of A.dl=surface integarl B.da] and explains how to find A using this equation. However, there is a statement by Griffiths that is not fully understood, which mentions a fat wire carrying a uniformly distributed current and a circumferential magnetic field. Further discussions revolve around justifying this statement and solving for the magnetic field of such a wire using Ampere's law. The conversation also suggests using LaTeX for easier reading of
  • #1
Kolahal Bhattacharya
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A solved problem from Griffiths creats problem.It requires some discussion...It asks to find vector potential of an infinite solenoid with n turns per unit length radius R and current I.
Griffiths correlates integral form of Ampere's law to [closed integral of A.dl=surface integarl B.da].I can find A from this, with B=(mu)nI,uniform axial field and A circumferential.
But Griffiths says something here which I cannot understand.Quoting him,"The present problem (with a uniform magnetic field (mu)nI inside the solenoid and no field outside) is analogous to the Ampere's law problem of a fat wire carrying a uniformly distributed current.The vector potential is 'circumferential' (it mimics the magnetic field of the wire)."
As it appears, Griffiths is talking about the case where a fat wire is carrying a line current.In this case, magnetiv field is circumferential...But what is its justification?
 
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Try solving the problem for starts. What's the magnetic field for such a wire? Hint: you can still use Ampere's law for it.

Also, it would be very helpful if you took at look at https://www.physicsforums.com/showthread.php?t=8997 It makes reading posts with math infinitely easier, and if you're going to be a physicist, you're going to have to learn LaTeX sooner or later, anyway.
 
  • #3


In this situation, it seems that Griffiths is trying to draw a comparison between the vector potential of an infinite solenoid and that of a fat wire carrying a line current. Both scenarios have a uniform magnetic field inside and no field outside. However, the key difference is the shape of the magnetic field.

In the case of the solenoid, the magnetic field is axial (parallel to the axis of the solenoid) and in the case of the fat wire, it is circumferential (perpendicular to the axis of the wire). Griffiths is pointing out that the vector potential for the solenoid mimics the magnetic field of the wire, hence it is also circumferential.

This comparison is justified by the fact that both situations involve a current-carrying object with a uniform magnetic field. The vector potential is a mathematical tool that helps us describe the magnetic field, and in this case, it is convenient to use the same form for both scenarios.

Furthermore, this comparison also highlights the idea of duality in electromagnetism. Duality refers to the interchangeability of electric and magnetic fields and their associated potentials. In this case, the vector potential for the solenoid is analogous to the electric potential for a charged wire, which also has a circumferential field.

In conclusion, Griffiths is highlighting the similarities between the vector potential for an infinite solenoid and a fat wire carrying a line current. This comparison is justified by the uniform magnetic fields in both scenarios and highlights the concept of duality in electromagnetism.
 

1. What is the problem being solved in Griffiths' work?

The problem being solved in Griffiths' work is a mathematical model for the motion of charged particles in electromagnetic fields.

2. What is the significance of this problem in the field of science?

This problem is significant because it allows for the prediction and understanding of the behavior of charged particles in a variety of physical systems, such as in electronics, plasma physics, and astrophysics.

3. How was this problem originally approached and solved?

This problem was originally approached using classical mechanics and Maxwell's equations of electromagnetism. It was solved using mathematical techniques such as differential equations and vector calculus.

4. What are some applications of this solved problem?

Some applications of this solved problem include the design and function of electronic devices, the study of plasma behavior in fusion reactors, and the understanding of charged particle interactions in space.

5. Are there any limitations to this solved problem?

Yes, there are limitations to this solved problem as it is a simplified model and does not take into account quantum effects. It also assumes ideal conditions and may not accurately describe real-world situations.

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