(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A magnetic field of a long straight wire carrying a currentIalong the z-axis is given by the following expression:

[tex] \mathbf{B} = \frac{\mu_0I}{2\pi} \{\frac{-y}{x^2+y^2} \hat{x} + \frac{y}{x^2 + y^2} \hat{y} \} [/tex]

Find two different potentials that will yield this field. Show explicitly that the curl of the difference between these two potentials vanishes.

2. Relevant equations

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

3. The attempt at a solution

I took a cross product to get this system...

[tex]

\frac{\partial A_y}{\partial x} - \frac{\partial A_x}{\partial y} = 0 \\

[/tex]

[tex]

\frac{\partial A_z}{\partial y} - \frac{\partial A_y}{\partial z} = \frac{-y}{x^2+y^2} \\

[/tex]

[tex]

\frac{\partial A_x}{\partial z} - \frac{\partial A_z}{\partial x} = \frac{y}{x^2+y^2} \\

[/tex]

I dont know what to do! Any ideas?

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# Homework Help: Find the vector potentials

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