If `4 xx 10^(20)eV` energy is required to move a charge of `0.25` coulomb between two points. Then what will be the potential difference between them ?

Options

A. 178 V
B. 256 V
C. 356 V
D. None of these

Answer

To find the potential difference between two points when a charge is moved, we can use the relationship between work done (or energy) and electric potential difference. The formula we will use is:

\[ V = \frac{W}{Q} \]

where:
- \( V \) is the potential difference,
- \( W \) is the work done (or energy required),
- \( Q \) is the charge.

### Step-by-step Solution:

1. **Identify the given values**:
- Energy required \( W = 4 \times 10^{20} \) eV
- Charge \( Q = 0.25 \) coulombs

2. **Convert energy from electron volts to joules**:
- We know that \( 1 \) eV \( = 1.6 \times 10^{-19} \) joules.
- Therefore, convert \( W \) to joules:
\[ W = 4 \times 10^{20} \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} \]
\[ W = 4 \times 1.6 \times 10^{20 - 19} \, \text{J} = 6.4 \times 10^{1} \, \text{J} = 64 \, \text{J} \]

3. **Calculate the potential difference**:
- Now, substitute the values into the formula:
\[ V = \frac{W}{Q} = \frac{64 \, \text{J}}{0.25 \, \text{C}} \]
\[ V = 256 \, \text{V} \]

4. **Conclusion**:
- The potential difference between the two points is \( 256 \, \text{V} \).

### Final Answer:
The potential difference between the two points is \( 256 \, \text{V} \).

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