Work done by a conservative force in bringing a body from infinity to A is 60 J and to B is 20J. What is the difference in potential energy between point A and B, i.e. `U_(B)-U_(A)`.

Explanation

To solve the problem, we need to find the difference in potential energy between points A and B, denoted as \( U_B - U_A \). We know the work done by a conservative force in bringing a body from infinity to points A and B.

### Step-by-step Solution:

1. **Understanding Work Done by Conservative Forces**:
The work done \( W \) by a conservative force when moving an object from a point at infinity to a point in the field is related to the change in potential energy \( U \) by the formula:
\[ W = -\Delta U = U_{\text{initial}} - U_{\text{final}} \]
Here, the initial point is at infinity where potential energy is considered to be zero.

2. **Calculate Potential Energy at Point A**:
Given that the work done in bringing the body from infinity to point A is 60 J, we can write:
\[ W_{A} = U_{\infty} - U_A \]
Since \( U_{\infty} = 0 \), we have:
\[ 60 = 0 - U_A \implies U_A = -60 \text{ J} \]

3. **Calculate Potential Energy at Point B**:
Similarly, for point B, the work done is 20 J:
\[ W_{B} = U_{\infty} - U_B \]
Again, since \( U_{\infty} = 0 \):
\[ 20 = 0 - U_B \implies U_B = -20 \text{ J} \]

4. **Find the Difference in Potential Energy**:
Now, we can find the difference in potential energy between points A and B:
\[ U_B - U_A = (-20) - (-60) \]
Simplifying this gives:
\[ U_B - U_A = -20 + 60 = 40 \text{ J} \]

### Final Answer:
The difference in potential energy between points A and B is:
\[ U_B - U_A = 40 \text{ J} \]