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Homework Statement
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.
Homework Equations
The Attempt at a Solution
A friend of mine had discovered this question somewhere on the Net. Unfortunately neither of us has any idea as to how to solve this problem. I think it involves Calculus to a degree,but I really don't know anything else about it. I would be truly grateful if somebody could kindly give me a full solution. Many, many thanks in advance!
PS. I just cannot understand why the LaTeX is not working. I'm really sorry for that.
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