# Dimensional Dilemma!

Consider an $$n$$-dimensional solid sphere of radius $$R$$, with uniform charge-density and a total charge $$Q$$. A charged particle $$q$$ is kept at a distance of $$r$$ from the center. For $$r<R$$, what is the Net Coulombic Force experienced by the particle?

If it is in the form of

$\displaystyle\vec{F_{c}}= \left(\dfrac{\color{blue}{m}}{\color{blue}{p}.\varepsilon_{0}}\right).\left(\dfrac{(\color{blue}{a}+2)!}{\left(\Gamma\left(\dfrac{\color{blue}{b}}{\color{blue}{c}}\right)\right)^{\color{blue}{x}}.\color{blue}{w^{y}}}\right)$

Find $$\color{blue}{ m+p+a+b+c+w+x+y}$$.

Details and Assumptions:

• $$n=12$$, $$Q=10 \text{ C}$$, $$q=1.4 \text{ C}$$, $$r=5 \text{ cm}$$, $$R=13\text{ cm}$$.

• All the letters represent integers and are not necessarily distinct. $$m$$ and $$n$$, $$b$$ and $$c$$ are coprime.

• $$\varepsilon_{0}$$ is the constant of permittivity of free space.

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