# Carbon Potential

**Electricity and Magnetism**Level 5

\[V(r) = \frac{Ze}{a\pi {\epsilon}_{0}} \left(\frac{1}{r} - \frac{b}{cR} + \frac{{r}^{2}}{d{R}^{3}}\right)\]

where \(R\) is the radius of the carbon atom, calculate \(Z+a+b+c+d\).

**Notes**

1) \(e\) is the charge of a proton

2) \({\epsilon}_{0}\) is the *permittivity of free space*

3) \(V(r)\) should not be confused with the potential energy, which would be of the form \[U(r) = -\frac{Z{e}^{2}}{a\pi {\epsilon}_{0}} \left(\frac{1}{r} - \frac{b}{cR} + \frac{{r}^{2}}{d{R}^{3}}\right)\]

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