The electric potential at. Point A is 20 V and B is – 20 V. The work done by an external force in moving electron slowly from B to A is

Options

A. (a)`-6.4 xx10^(-18)J`
B. (b)`+6.4 xx10^(-18)J`
C. (c)`+4xx10^(-20)J`
D. (d)`-4xx10^(-20)J`

Answer

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

### Step-by-Step Solution:

1. **Identify the Electric Potentials:**
- The electric potential at point A (V_A) is given as 20 V.
- The electric potential at point B (V_B) is given as -20 V.

2. **Understand the Work Done Formula:**
- The work done (W) by an external force in moving a charge (Q) in an electric field is given by the formula:
\[ W = Q \cdot (V_A - V_B) \]
- Here, \(V_A\) is the potential at point A, and \(V_B\) is the potential at point B.

3. **Determine the Charge of the Electron:**
- The charge of an electron (Q) is approximately:
\[ Q = -1.6 \times 10^{-19} \, \text{C} \]

4. **Calculate the Potential Difference:**
- Substitute the values of \(V_A\) and \(V_B\) into the formula for potential difference:
\[ V_A - V_B = 20 - (-20) = 20 + 20 = 40 \, \text{V} \]

5. **Calculate the Work Done:**
- Now substitute the charge and the potential difference into the work done formula:
\[ W = (-1.6 \times 10^{-19}) \cdot (40) \]
- Performing the multiplication:
\[ W = -6.4 \times 10^{-18} \, \text{J} \]

6. **Conclusion:**
- The work done by the external force in moving the electron from point B to point A is:
\[ W = -6.4 \times 10^{-18} \, \text{J} \]

### Final Answer:
The work done by an external force in moving the electron slowly from B to A is \(-6.4 \times 10^{-18} \, \text{J}\).

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