Problem with Net Coulombic Force

[Better WOrld]

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.

 

[Doc Al]

PS. I just cannot understand why the LaTeX is not working. I'm really sorry for that.

Take a look at this: https://www.physicsforums.com/help/latexhelp/

 

[Better WOrld]

Take a look at this: https://www.physicsforums.com/help/latexhelp/

Thanks a lot Sir! Sir, please could you answer my question? Many thanks Sir!

 

[Doc Al]

Consider an ## n ##-dimensional solid sphere of radius ##R##, with uniform charge-density and a total charge ##Q##.

A 12-dimensional sphere with uniform charge density? I have no idea what that even means.

Where did you get this problem?

 

[Better WOrld]

A 12-dimensional sphere with uniform charge density? I have no idea what that even means.

Where did you get this problem?

Sir, a friend of mine had come across this problem. I'm afraid I don't know where he found it.