Which interaction has the **highest** electrostatic potential energy?

Group of answer choices

A +1 and -1 particle separated by a distance of 5 nm.

A +2 and +2 particle separated by a distance of 10 nm.

A +2 and +2 particle separated by a distance of 100 nm.

A +2 and +2 particle separated by a distance of 5 nm.

To determine which interaction has the highest electrostatic potential energy, we can use the formula for electrostatic potential energy between two point charges:

\[
U = \frac{k \cdot q_1 \cdot q_2}{r}
\]

where:
- \(U\) is the electrostatic potential energy,
- \(k\) is Coulomb's constant (\(8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2\)),
- \(q_1\) and \(q_2\) are the charges of the particles, and
- \(r\) is the distance between the charges.

### Let's evaluate each option:

1. **A +1 and -1 particle separated by a distance of 5 nm**:
   \[
   U_1 = \frac{k \cdot (+1) \cdot (-1)}{5 \times 10^{-9}} = \frac{-k}{5 \times 10^{-9}}
   \]

2. **A +2 and +2 particle separated by a distance of 10 nm**:
   \[
   U_2 = \frac{k \cdot (+2) \cdot (+2)}{10 \times 10^{-9}} = \frac{4k}{10 \times 10^{-9}} = \frac{2k}{5 \times 10^{-9}}
   \]

3. **A +2 and +2 particle separated by a distance of 100 nm**:
   \[
   U_3 = \frac{k \cdot (+2) \cdot (+2)}{100 \times 10^{-9}} = \frac{4k}{100 \times 10^{-9}} = \frac{k}{25 \times 10^{-9}}
   \]

4. **A +2 and +2 particle separated by a distance of 5 nm**:
   \[
   U_4 = \frac{k \cdot (+2) \cdot (+2)}{5 \times 10^{-9}} = \frac{4k}{5 \times 10^{-9}}
   \]

### Comparison of results:
- \( U_1 = -\frac{k}{5 \times 10^{-9}} \)
- \( U_2 = \frac{2k}{5 \times 10^{-9}} \)
- \( U_3 = \frac{k}{25 \times 10^{-9}} \)
- \( U_4 = \frac{4k}{5 \times 10^{-9}} \)

The magnitude of the potential energy is highest for the interaction involving two +2 charges separated by 5 nm, which is **option 4**.

So, the correct answer is:

**A +2 and +2 particle separated by a distance of 5 nm.**

Would you like further clarification or details on this? Here are some related questions to expand on this topic:

1. How does the sign of charges affect electrostatic potential energy?
2. What role does the distance between charges play in determining electrostatic force?
3. How would the potential energy change if the charges were -2 and -2 instead of +2 and +2?
4. Can electrostatic potential energy ever be zero between two charges?
5. What is the physical significance of negative electrostatic potential energy?

**Tip:** The closer the charges are, the stronger the electrostatic interaction, and the higher the potential energy.

Which interaction has the highest electrostatic potential energy? Group of answer choices: A +1 and -1 particle separated by a distance of 5 nm. A +2 and +2 particle separated by a distance of 10 nm. A +2 and +2 particle separated by a distance of 100 nm. A +2 and +2 particle separated by a distance of 5 nm.

Explore how to determine which interaction has the highest electrostatic potential energy using Coulomb's Law. The problem compares various charge interactions, including +1 and -1 particles and +2 and +2 particles at different distances. Suitable for Grades 10-12 students learning electrostatics.

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