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A charge of [tex]$-4.33 \times 10^{-6} \, \text{C}$[/tex] is located [tex]0.525 \, \text{m}[/tex] from a charge of [tex]$-7.81 \times 10^{-4} \, \text{C}$[/tex]. What is their electric potential energy? Include the correct sign (+ or -).

(Unit: J)


Sagot :

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].