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Oct 5, 2023 at 10:54 history removed from network questions Qmechanic
Oct 5, 2023 at 8:53 history became hot network question
Oct 5, 2023 at 1:59 vote accept Jack
Oct 5, 2023 at 1:39 comment added hyportnex yes $\mathbf {grad}(1.78)=\mathbf 0$
Oct 5, 2023 at 1:38 comment added Jack @hyportnex the curl of the magnetic force is zero when the magnetic field is static, does that mean I can write it as grad f?
Oct 5, 2023 at 1:33 comment added hyportnex even if you call the magnetic force on a charge a field, which is your right to do as you may call your breakfast a field, too, it is not $\mathbf A = \mathbf {f(\dot r)}$ but rather $\mathbf A = \mathbf {f(\dot r, r)}$ in which case its curl is not zero with respect to either variable.
Oct 5, 2023 at 1:27 comment added Jack @Buzz but the magnetic force depend on the magnetic field in addition to their dependence on velocity, and both the velocity and the magnetic field can be position dependant, that is to say, the magnetic force depends implicitly on position, doesn't it?
Oct 5, 2023 at 1:27 answer added Maximal Ideal timeline score: 5
Oct 5, 2023 at 1:21 answer added S.G timeline score: 8
Oct 5, 2023 at 1:15 comment added Buzz A field is, by definition, a function a $\mathbf{r}$. For example, magnetic force is not a field, because it does not have this property, as it depends on the velocity of the charge experiencing the force, which is itself not something that is defined at arbitrary $\mathbf{r}$, but only at the location of the charge in question.
Oct 5, 2023 at 1:06 comment added Jack @MaximalIdeal I meant $\textbf{A}=\textbf{A}(\frac{d\textbf{r}}{dt})$ something like the magnetic force field which is a velocity dependent field.
Oct 5, 2023 at 1:03 comment added Maximal Ideal @Jack Also, sorry to ask, but can you clarify what you mean when you write $\textbf{A}=\textbf{A}(\dot{\textbf{r}})$?
Oct 5, 2023 at 1:01 comment added Jack @hyportnex so it doesn't matter weather $\textbf{A}=\textbf{A}(\textbf{r})$ or $\textbf{A}=\textbf{A}(\dot{\textbf{r}})$, we can always write $\textbf{A}$ as grad $\psi$ locally?
Oct 5, 2023 at 0:57 history edited Jack CC BY-SA 4.0
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Oct 5, 2023 at 0:56 comment added hyportnex it is true locally in a sufficiently small neighborhood
Oct 5, 2023 at 0:53 history asked Jack CC BY-SA 4.0