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 the 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 solve the question of identifying the wrong statement regarding electric potential energy, we will analyze each option step by step.

### Step 1: Understanding Electric Potential Energy
Electric potential energy (U) in a system of charges depends on the positions of the charges and the work done in bringing them from infinity to their positions. The change in electric potential energy (ΔU) can be calculated based on the work done by the electrostatic forces.

### Step 2: Analyzing Each Option

**Option A:** "The electric potential energy of the system of two protons shall increase if the separation between the two is decreased."
- **Analysis:** When two protons are brought closer together, they repel each other due to their like charges. The work done against this repulsive force is negative, leading to an increase in potential energy. Thus, this statement is **correct**.

**Option B:** "The electric potential energy of the proton-electron system will increase if the separation between them is decreased."
- **Analysis:** A proton and an electron attract each other. When they are brought closer together, the work done by the electrostatic force is positive, resulting in a decrease in potential energy. Therefore, this statement is **incorrect**.

**Option C:** "The electric potential energy of the proton-electron system will increase if the separation between them is increased."
- **Analysis:** As the separation between a proton and an electron increases, work is done against the attractive force, which is negative. This results in an increase in potential energy. Thus, this statement is **correct**.

**Option D:** "The electric potential energy of the system of two electrons will increase if the separation between them is decreased."
- **Analysis:** Two electrons repel each other. When they are brought closer, work is done against the repulsive force, resulting in an increase in potential energy. Thus, this statement is **correct**.

### Conclusion
After analyzing all options, we find that **Option B** is the wrong statement.