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Problem with Net Coulombic Force

  1. Jul 28, 2015 #1
    1. The problem statement, all variables and given/known data
    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.
    2. Relevant equations


    3. 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.
     
    Last edited: Jul 28, 2015
  2. jcsd
  3. Jul 28, 2015 #2

    Doc Al

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    Staff: Mentor

  4. Jul 28, 2015 #3
  5. Jul 28, 2015 #4

    Doc Al

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    Staff: Mentor

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

    Where did you get this problem?
     
  6. Jul 28, 2015 #5
    Sir, a friend of mine had come across this problem. I'm afraid I don't know where he found it.
     
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