- #1

Petar Mali

- 290

- 0

[tex]\Delta\vec{A}-\frac{1}{c^2}\frac{\partial^2 \vec{A}}{\partial t^2}=-\mu_0\vec{j}[/tex]

[tex]\Delta\varphi-\frac{1}{c^2}\frac{\partial^2 \varphi}{\partial t^2}=-\frac{1}{\epsilon_0}\rho[/tex]

[tex]c=\frac{1}{\sqrt{\epsilon_0\mu_{0}}}[/tex]

[tex]\epsilon_0=8,85\cdot 10^{-12}\frac{F}{m}[/tex]

[tex]\mu_0=4\pi 10^{-7}T[/tex]

[tex]div\vec{A}+\frac{1}{c^2}\frac{\partial \varphi}{\partial t}=0[/tex]

[tex]\frac{\partial A_x}{\partial x}+\frac{\partial A_y}{\partial _y}+\frac{\partial A_z}{\partial z}+\frac{\partial (\frac{1}{c}\varphi)}{\partial (ct)}=0[/tex]

[tex]A^{\mu}=(\vec{A},\frac{1}{c}\varphi)[/tex]

[tex]A_{\mu}=g_{\mu\nu}A^{\nu}[/tex]

[tex]A_{\mu}=(-\vec{A},\frac{1}{c}\varphi)[/tex]

[tex]divA^{\mu}=0[/tex]

[tex]j^{\mu}=(j_x,j_y,j_z,c\rho)[/tex]

[tex]\Delta\varphi-\frac{1}{c^2}\frac{\partial^2 \varphi}{\partial t^2}=-\frac{1}{\epsilon_0}\rho[/tex]

[tex]c=\frac{1}{\sqrt{\epsilon_0\mu_{0}}}[/tex]

[tex]\epsilon_0=8,85\cdot 10^{-12}\frac{F}{m}[/tex]

[tex]\mu_0=4\pi 10^{-7}T[/tex]

[tex]div\vec{A}+\frac{1}{c^2}\frac{\partial \varphi}{\partial t}=0[/tex]

[tex]\frac{\partial A_x}{\partial x}+\frac{\partial A_y}{\partial _y}+\frac{\partial A_z}{\partial z}+\frac{\partial (\frac{1}{c}\varphi)}{\partial (ct)}=0[/tex]

[tex]A^{\mu}=(\vec{A},\frac{1}{c}\varphi)[/tex]

[tex]A_{\mu}=g_{\mu\nu}A^{\nu}[/tex]

[tex]A_{\mu}=(-\vec{A},\frac{1}{c}\varphi)[/tex]

[tex]divA^{\mu}=0[/tex]

**Can I say from**

[tex]A^{\mu}=(\vec{A},\frac{1}{c}\varphi)[/tex]

and

[tex]A_{\mu}=(-\vec{A},\frac{1}{c}\varphi)[/tex]

something more about gauge transformations of electromagnetic potentials

[tex]\varphi_0=\varphi-\frac{\partial f}{\partial t}[/tex]

[tex]\vec{A}_0=\vec{A}+gradf[/tex]

I think about - sign in first term [tex]-\frac{\partial f}{\partial t}[/tex] and + sign in second term [tex]+gradf[/tex][tex]A^{\mu}=(\vec{A},\frac{1}{c}\varphi)[/tex]

and

[tex]A_{\mu}=(-\vec{A},\frac{1}{c}\varphi)[/tex]

something more about gauge transformations of electromagnetic potentials

[tex]\varphi_0=\varphi-\frac{\partial f}{\partial t}[/tex]

[tex]\vec{A}_0=\vec{A}+gradf[/tex]

I think about - sign in first term [tex]-\frac{\partial f}{\partial t}[/tex] and + sign in second term [tex]+gradf[/tex]

**Or**

[tex]\varphi_0=\varphi+\frac{\partial f}{\partial t}[/tex]

[tex]\vec{A}_0=\vec{A}-gradf[/tex]

[tex]\Delta A^{\mu}-\frac{1}{c^2}\frac{\partial^2 A^{\mu}}{\partial t^2}=-\mu_0j^{\mu}[/tex][tex]\varphi_0=\varphi+\frac{\partial f}{\partial t}[/tex]

[tex]\vec{A}_0=\vec{A}-gradf[/tex]

[tex]j^{\mu}=(j_x,j_y,j_z,c\rho)[/tex]

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