To calculate the electric potential energy between two point charges, we use the formula:
[tex]\[ U = \frac{k \cdot q_1 \cdot q_2}{r} \][/tex]
where:
- [tex]\( U \)[/tex] is the electric potential energy,
- [tex]\( k \)[/tex] is Coulomb's constant ([tex]\( k = 8.988 \times 10^9 \, \text{N m}^2 / \text{C}^2 \)[/tex]),
- [tex]\( q_1 \)[/tex] is the first charge ([tex]\( q_1 = -4.33 \times 10^{-6} \, \text{C} \)[/tex]),
- [tex]\( q_2 \)[/tex] is the second charge ([tex]\( q_2 = -7.81 \times 10^{-4} \, \text{C} \)[/tex]),
- [tex]\( r \)[/tex] is the separation distance ([tex]\( r = 0.525 \, \text{m} \)[/tex]).
We plug in the values into the formula as follows:
[tex]\[ U = \frac{(8.988 \times 10^9) \cdot (-4.33 \times 10^{-6}) \cdot (-7.81 \times 10^{-4})}{0.525} \][/tex]
Upon calculation, the result is:
[tex]\[ U = 57.8952176 \, \text{J} \][/tex]
The correct sign for the potential energy between two like charges (both negative in this case) is positive. Therefore, the electric potential energy is:
[tex]\[ \boxed{57.8952176 \, \text{J}} \][/tex]
Thus, the electric potential energy between the two charges is [tex]\( 57.8952176 \, \text{J} \)[/tex].
