The solid metal sphere of radius $a=0\mathrm{.}200m$ shown in the figure has a surface charge distribution of $.$ The potential difference between the surface of the sphere and

a point $P$ at a distance $r_P=0\mathrm{.}383m$ from the center of the sphere is $V=V_{\text{s}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}}-V_P=+18\mathrm{.}5V.$ Determine the value of $.$

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