I am trying to express the Maxwell equation $$ \partial_a F^{ab} = \mu_0 J^b $$ in cylindrical coordinates. Now, if I express this equation for b=0, the a's would get summed up as $$ \partial_0 F^{00} + \partial_1 F^{10} + \partial_2 F^{20} + \partial_3 F^{30} = \mu_0 J^0 $$  Now in cylindrical coordinates 0,1,2,3 corresponds to t, r, $\phi$, z respectively. The first term would be zero since $F^{00}=0$.    My doubt is whether I can write the other terms simply as partial derivatives w.r.t. r, $\phi$, z respectively as $$\frac{\partial F^{10}}{\partial r} + \frac{\partial F^{20}}{\partial \phi} + \frac{\partial F^{30}}{\partial z}=\mu_0 J^0$$  Usually standard texts only give the information for gradiant, divergence and curl in cylindrical coordinates and not to such partial derivatives.
I understand that the  is given by  $$F^{\mu\nu}\mapsto\begin{pmatrix}0 &amp; -E_{x} &amp; -E_{y} &amp; -E_{z}\\ E_{x} &amp; 0 &amp; -B_{z} &amp; B_{y}\\ E_{y} &amp; B_{z} &amp; 0 &amp; -B_{x}\\ E_{z} &amp; -B_{y} &amp; B_{x} &amp; 0 \end{pmatrix}$$  where $\mu$, $\nu$ can take the values {0,1,2,3} or {$t,x,y,z$}.  So, for example  $$F^{01}=F^{tx}=-E_x$$  My question is, what would the following expression be?  $$F^{t\rho}=?$$ or $$F^{z\rho}=?$$  where $\rho=\sqrt{x^{2}+y^{2}}$ is the radial coordinate in ?  And more generally, how can we construct the Electromagnetic Tensor in cylindrical coordinates? Where $\mu$, $\nu$ now take the values {$t,\rho,\varphi,z$}.
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Image of concave mirror when object is farther than the focal point I have a set of concave/convex mirrors/lenses, and I have drawn out all of the ray tracing diagrams for each possible combination and type of image each optical element can produce. When I look at the ray tracing diagrams then reproduce the situation in the real world with myself as the &quot;object&quot;, all the scenarios make sense to me except one: when I as the object stand beyond the focal point of a concave mirror.  The image ends up as &quot;real&quot; and appears to be in front of the mirror. Now I understand that in the situation above, I as the object would stand at 6m and this would result in the image appearing at 12m. So if I placed a wall or screen at the 12m mark, the image would form on that surface (just like a movie theater screen).... at least I think I interpreted that correctly. But I still see myself when I look in the mirror?! 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I have tries lot of things but nothing worked.  can somebody tell me how to solve this problem? Is there a regular expression to validate an email address in JavaScript? In how many ways can we choose $r$ numbers from $\{1,2,3,...,n\}$,   In a way where we have no consecutive numbers in the set? (like $1,2$) multiline command chunks in bash history into multiple lines In Bash (as well as Bash in WSL), multiline written commands can call-back with up/down arrows correctly also built-in history command report them correctly (until I'm still logged-in in bash). But after exiting from bash and press up/down arrows, multiline commands appears each as separate entries and that's because cat ~/.bash_history has chucked the command on multiple separate entries and writing problem here; the history command result messed too. 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