The electric potential at point `A` is `20 V` and at `B` is `-40 V`. Find the work done by an external and electrostatic force in moving an electron slowly from B to A.

Explanation

To solve the problem of finding the work done by an external force and the electrostatic force in moving an electron from point B to point A, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Charge of the Electron**:
The charge of an electron (Q₀) is given as:
\[ Q₀ = -1.6 \times 10^{-19} \text{ C} \]

2. **Identify the Electric Potentials**:
The electric potential at point A (V_A) and point B (V_B) are given as:
\[ V_A = 20 \text{ V} \]
\[ V_B = -40 \text{ V} \]

3. **Calculate the Work Done by the External Force**:
The work done (W_ext) by the external force in moving the charge from B to A can be calculated using the formula:
\[ W_{\text{ext}} = Q₀ \times (V_A - V_B) \]
Substituting the values:
\[ W_{\text{ext}} = -1.6 \times 10^{-19} \times (20 - (-40)) \]
\[ = -1.6 \times 10^{-19} \times (20 + 40) \]
\[ = -1.6 \times 10^{-19} \times 60 \]
\[ = -9.6 \times 10^{-18} \text{ J} \]

4. **Calculate the Work Done by the Electrostatic Force**:
The work done by the electrostatic force (W_elec) is equal to the negative of the work done by the external force:
\[ W_{\text{elec}} = -W_{\text{ext}} \]
Substituting the value we found:
\[ W_{\text{elec}} = -(-9.6 \times 10^{-18}) = 9.6 \times 10^{-18} \text{ J} \]

### Final Results:
- Work done by the external force:
\[ W_{\text{ext}} = -9.6 \times 10^{-18} \text{ J} \]
- Work done by the electrostatic force:
\[ W_{\text{elec}} = 9.6 \times 10^{-18} \text{ J} \]