Vector Potential: Analyzing the Lines of Force & B Direction

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Discussion Overview

The discussion revolves around the vector potential (A) defined as A = xj - yi, exploring the implications for the lines of force and the direction of magnetic induction (B) in a specified region of space. Participants engage in technical reasoning regarding the computation of the curl and its relationship to B, as well as the interpretation of lines of force associated with the vector field.

Discussion Character

  • Technical explanation, Conceptual clarification, Mathematical reasoning

Main Points Raised

  • One participant presents the vector potential A and inquires about the appearance of lines of force and the direction of B.
  • Another participant suggests computing the curl of A and equating it to B as a method to determine its direction.
  • A request for clarification on how to compute the curl and references to Griffith's book are made, indicating a need for guidance on the topic.
  • Participants discuss the relationship between the vector potential and the lines of force, noting that the vector field is tangent to its lines of force.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants explore different aspects of the vector potential and its implications without settling on a definitive explanation of the lines of force or the direction of B.

Contextual Notes

Participants express uncertainty about the specific computational steps involved in finding the curl and its implications for the lines of force, indicating a reliance on external resources for clarification.

Who May Find This Useful

Individuals interested in vector potentials, magnetic fields, and their mathematical descriptions, particularly students or practitioners in physics and engineering fields.

Reshma
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The vector potential (A) in a certain region is given by A = xj-yi where i and j are unit vectors.

How will the lines of force look like?

What is the direction of magnetic induction B in the given region of space?
 
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How about computing the curl and setting it equal to B?

Daniel.
 
Can please you explain me how you do that? Can you point out to me a chapter in Griffith's book which might help?
 
Yes,it surely is the one in which this pops up

[tex]\vec{B}=\nabla\times \vec{A}[/tex]

Daniel.
 
Yes, but how does it explain the lines of force?
 
Find the vector fields,its components and then u know that this vector field is always tangent to its lines of force...

Daniel.
 
OK, thanks for the help :-)
 

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