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## Main Question or Discussion Point

[tex]\vec{B}=rot\vec{A}[/tex]

[tex]\vec{E}=-\frac{\partial\vec{A}}{\partial t}-grad\varphi[/tex]

If I define

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

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

where

[tex]f=f(x,y,z,t)[/tex]

I will get

[tex]\vec{B}=rot\vec{A}=rot\vec{\widetilde{\vec{A}}}[/tex]

[tex]\vec{E}=-\frac{\partial\vec{A}}{\partial t}-grad\varphi=-\frac{\partial\widetilde{\vec{A}}}{\partial t}-grad\widetilde{\varphi}[/tex]

But if I say

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

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

I wouldnt get that result. How I know how to take minus sign in this relations!

[tex]\vec{E}=-\frac{\partial\vec{A}}{\partial t}-grad\varphi[/tex]

If I define

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

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

where

[tex]f=f(x,y,z,t)[/tex]

I will get

[tex]\vec{B}=rot\vec{A}=rot\vec{\widetilde{\vec{A}}}[/tex]

[tex]\vec{E}=-\frac{\partial\vec{A}}{\partial t}-grad\varphi=-\frac{\partial\widetilde{\vec{A}}}{\partial t}-grad\widetilde{\varphi}[/tex]

But if I say

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

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

I wouldnt get that result. How I know how to take minus sign in this relations!