A charged partile is moved infinitesimally slowly from point A to B in a region of space containing electric field by an external agent. Work done by the external agent is 50 J . Two students calculate the potential energy of the particle at A and B. Student X reports to the teacher the values of potential energy at A and B are 50 J and 100 J while student Y reports then to be 70 J and 120 J . Which of the two students is wrong

Options

A. X
B. Y
C. Both are correct
D. Both are incorrect

Answer

To solve the problem, we need to analyze the work done by the external agent and how it relates to the potential energy at points A and B.

### Step-by-Step Solution:

1. **Understanding Work Done and Potential Energy**:
- The work done by the external agent when moving a charged particle from point A to point B is given as 50 J.
- Since the particle is moved slowly, we can assume that the change in kinetic energy (ΔKE) is zero. Thus, all the work done goes into changing the potential energy (ΔU).

2. **Relating Work Done to Change in Potential Energy**:
- The relationship can be expressed as:
\[ W = \Delta U \]
- Here, \(W\) is the work done (50 J), and \(\Delta U\) is the change in potential energy, which can be calculated as:
\[ \Delta U = U_B - U_A \]
- Therefore, we have:
\[ U_B - U_A = 50 \text{ J} \]

3. **Evaluating Student X's Values**:
- Student X reports:
- \(U_A = 50 \text{ J}\)
- \(U_B = 100 \text{ J}\)
- Calculating the change in potential energy:
\[ \Delta U = U_B - U_A = 100 \text{ J} - 50 \text{ J} = 50 \text{ J} \]
- This matches the work done (50 J), so Student X's values are correct.

4. **Evaluating Student Y's Values**:
- Student Y reports:
- \(U_A = 70 \text{ J}\)
- \(U_B = 120 \text{ J}\)
- Calculating the change in potential energy:
\[ \Delta U = U_B - U_A = 120 \text{ J} - 70 \text{ J} = 50 \text{ J} \]
- This also matches the work done (50 J), so Student Y's values are also correct.

5. **Conclusion**:
- Both students have calculated the potential energy values correctly since both yield a change in potential energy of 50 J, which is equal to the work done by the external agent.

### Final Answer:
Both students are correct.