# Problem with Net Coulombic Force

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1. Jul 28, 2015

### Better WOrld

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. Jul 28, 2015

### Staff: Mentor

3. Jul 28, 2015

### Better WOrld

4. Jul 28, 2015

### Staff: Mentor

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

Where did you get this problem?

5. Jul 28, 2015

### Better WOrld

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