Identify the wrong statement

Options

A. The electrical potential energy of a system of two protons shall increase if the separation between the two is decreased
B. The electrical potential energy of a proton-electron system will increase if the separation between the two is decreased
C. The electrical potential energy of a proton-electron system will increase if thee separation between the two is increased
D. The electrical potential energy of system of two electrons shall increase if the separation between the two is decreased.

Answer

To identify the wrong statement regarding electric potential energy in systems of charges, we can analyze the behavior of potential energy in relation to the distance between charges.

### Step-by-Step Solution:

1. **Understanding Electric Potential Energy**:
- The electric potential energy (U) between two point charges is given by the formula:
\[ U = k \frac{q_1 q_2}{r} \]
where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between them.

2. **Analyzing Same Polarity Charges**:
- For two charges of the same polarity (e.g., two protons or two electrons), the force between them is repulsive.
- If the distance \( r \) between them decreases, the potential energy increases because you are moving against the direction of the repulsive force.
- Thus, the statement that "the electric potential energy of the system of two protons increases if the separation between them is decreased" is **correct**.

3. **Analyzing Opposite Polarity Charges**:
- For two charges of opposite polarity (e.g., a proton and an electron), the force between them is attractive.
- If the distance \( r \) decreases, the potential energy decreases because you are moving in the direction of the attractive force.
- Therefore, the statement that "the electric potential energy of the system of two opposite charges increases if the separation between them is decreased" is **incorrect**.

4. **Conclusion**:
- The wrong statement is the one that suggests that the potential energy increases when the separation between two opposite charges is decreased. This is contrary to the behavior of electric potential energy in such systems.

### Final Answer:
The wrong statement is **B**: "The electric potential energy of the system of two opposite charges increases if the separation between them is decreased."

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