- #1
Petar Mali
- 290
- 0
[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 wouldn't 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 wouldn't get that result. How I know how to take minus sign in this relations!