A proton is nearly 1,836 times more massive than the electron. The Coulomb force of repulsion between two protons separated by a finite distance is F. The electrostatic force between two electrons separated by the same distance is:

Options

A. F
B. `F/(1,837)`
C. 1,837 F
D. `(1,837)/F`

Answer

To solve the problem, we need to determine the electrostatic force between two electrons when the Coulomb force of repulsion between two protons is given as F.

### Step-by-Step Solution:

1. **Understanding Coulomb's Law**:
According to Coulomb's law, the electrostatic force (F) between two point charges is given by the formula:
\[ F = k \frac{q_1 q_2}{r^2} \]
where \( k \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the charges.

2. **Force Between Protons**:
For two protons, each with a charge of \( +e \):
\[ F = k \frac{(+e)(+e)}{r^2} = k \frac{e^2}{r^2} \]
We are given that this force is \( F \).

3. **Force Between Electrons**:
For two electrons, each with a charge of \( -e \):
\[ F' = k \frac{(-e)(-e)}{r^2} = k \frac{e^2}{r^2} \]
Here, the negative signs cancel out, resulting in a positive force, indicating repulsion.

4. **Comparing Forces**:
Since both forces (between protons and between electrons) are expressed in the same form:
\[ F' = k \frac{e^2}{r^2} = F \]
Therefore, the electrostatic force between two electrons is equal to the force between two protons.

5. **Conclusion**:
Thus, the electrostatic force between two electrons separated by the same distance is also \( F \).

### Final Answer:
The electrostatic force between two electrons is \( F \).

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