A curve segment LLL$,$ defined by the equations z$=0$z $=0$z$=0,$ x$2+$y$2=$a$2$x$^2+$ y$^2=$ a$^2$x$2+$y$2=$a$2,$ and x$,$y in $[0,$a$]$x$,$ y $\backslash$in $[0,$ a$]$x$,$y in $[0,$a$],$ a$>0$a $>0$a$>0,$ is located in space. This curve segment carries a total charge QQQ uniformly distributed along it$.$

a$)$ Write the explicit expression for the volume charge density $\backslash$rho corresponding to this charge distribution.

b$)$ Calculate the electric field E$\backslash$mathbf$\{$E$\}$E at the point P$(0,0,0)$P$(0,0,0)$P$(0,0,0).$

c$)$ Compute separately the force exerted on a point charge qqq$,$ placed at P$(0,0,0)$P$(0,0,0)$P$(0,0,0),$ by the total charge QQQ on the curve segment LLL$,$ and the force exerted by the point charge qqq on the charge QQQ distributed along the curve LLL$.$ Discuss the results.