Question

Two point charges 2.0 cm apart have an electric potential energy -180 mJ. The total charge is 30 nC. What are the two charges?

Short answer

The charges value of two points are 40nC and -10nC

Step-by-step solution

Step  1: Definition the equation of the potential energy of  a  point 

For the Two charge points

$$\begin{gathered} U=1/\left(4\pi {\epsilon }_0\right)\frac{q_1{q}_2}{r} \\ U=-180\mu J \\ r=2cm \\ {\epsilon }_0=8.85\times {10}^{-12}{C}^2/N\times m^2 \\ U=1/\left(4\pi {\epsilon }_0\right)\frac{q_1{q}_2}{r} \\ -180\mu J=1/\left(4\pi {\epsilon }_0\right)\frac{q_1{q}_2}{r} \\ {q}_1{q}_2=\left(-180\mu J\right)\left(8.85\times {10}^{-12}{C}^2/N\times m^2\right)\left(2cm\right)=-4\times {10}^{-16}{C}^2 \end{gathered}$$

As per the basis of the question

localid="1648127293201" $q_1=30\times {10}^{-9}C-q_2$

Now, applying given value of $q_2$in above equation

$q_2=-1\times {10}^{-8}C=-10nC$

Definition the equation of the potential energy of  two points

Applying the value of $q_{2}in{q}_{1}equation$

$q_1=40nC$

The charges values of two points are 40 nC and -10 nC