# Dimensional Dilemma!

**Electricity and Magnetism**Level 5

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.