Let A$\backslash$mathbf$\{$A$\}$A be the vector potential and B$\backslash$mathbf$\{$B$\}$B the magnetic field of the infinite solenoid of radius RRR$.$ Then

B$($r$)=\{0$if$$r$>$RBkif$$r R $\backslash \backslash$ B$\backslash$mathbf$\{$k$\}$ & $\backslash$text$\{$if $\}$ r $<$ R $\backslash$end$\{$cases$\}$B$($r$)=\{0$Bk$$if$$r$>$Rif$$rR$12$B$$y$,$x$,0$if$$r R $\backslash \backslash \backslash$frac$\{1\}\{2\}$ B $\backslash$langle $-$y$,$ x$,0\backslash$rangle & $\backslash$text$\{$if $\}$ r $<$ R $\backslash$end$\{$cases$\}$A$($r$)=\{21$R$2$B$$r$2$y$,$r$2$x$,021$B$$y$,$x$,0$if$$r$>$Rif$$r