Why Does Equation (7) in Magnetic Vector Potential Have a Negative Sign?

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SUMMARY

The discussion centers on the negative sign in Equation (7) of the Magnetic Vector Potential as presented in Griffith's 4th edition textbook. The user seeks clarification on why this negative sign is necessary, especially after obtaining a solution in Equation (5). It is established that Equation (5) does not represent the vector potential but rather the integral of the magnetic field over a specified area, which is linked to the vector potential through a line integral. The distinction between Equations (5) and (6) is crucial for understanding the derivation of the vector potential.

PREREQUISITES
  • Understanding of vector calculus as applied in electromagnetism
  • Familiarity with Griffith's Introduction to Electrodynamics, 4th edition
  • Knowledge of magnetic fields and vector potentials
  • Basic principles of line integrals in physics
NEXT STEPS
  • Review the derivation of the Magnetic Vector Potential in Griffith's textbook
  • Study the relationship between magnetic fields and vector potentials
  • Learn about line integrals and their applications in electromagnetism
  • Examine the differences between various equations in the context of vector potential solutions
USEFUL FOR

Students preparing for exams in electromagnetism, physics educators, and anyone seeking a deeper understanding of vector potentials and their mathematical representations.

fricke
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Not a homework question! I am doing exercises for upcoming final exam.

So, I get stuck at question 5.27 (Griffith 4th edition textbook).

Question:
Find the vector potential above and below an infinite uniform surface current with constant current sheet, K flowing at positive x direction.

I get really stuck so I googled the answer and it shows like this:
http://www.physicspages.com/2013/03/11/magnetic-vector-potential-of-an-infinite-wire/

What I don't understand is, from the link there, why does equation (7) need negative sign? I mean, we already obtain a nice solution in equation (5).

Help me please, thank you.
 
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fricke said:
Not a homework question! I am doing exercises for upcoming final exam.

That counts as homework as far as Physics Forums is concerned. This thread has been moved accordingly.

fricke said:
why does equation (7) need negative sign? I mean, we already obtain a nice solution in equation (5).

Equation (5) is not a solution for the vector potential, which is what you are supposed to find. It's a solution for the integral of the magnetic field over a given area, which is equal to the line integral of the vector potential around its boundary. Try comparing equation (5) with equation (6).
 

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