Question

Point charges create equipotential lines that are circular around the charge (in the plane of the paper). What is the potential energy, in nJ, of a 1 nC charge located 2.82 m from a 2 nC charge ?

Answer 1

The potential energy U of a system formed by two point charges separated a distance r is:

$U=k\frac{q_1q_2}{r}$

Where k is Coulomb's Constant:

$k=8.98755\times10^9N\frac{m^2}{C^2}$

Repace q1=1nC, q2=2nC and r=2.82m to find the potential energy of the system:

$\begin{gathered} U=k\frac{q_1q_2}{r} \\ \\ =(8.98755\times10^9N\frac{m^2}{C^2})\times\frac{(1\times10^{-9}C)(2\times10^{-9}C)}{2.82m} \\ \\ =6.3741489...\times10^{-9}Nm \\ \\ \approx6.37nJ \end{gathered}$

Therefore, the potential energy of the system is approximately 6.37 nanoJoules.