The force of repulsion between two electrons at a certain distance is F. The force between two protons separated by the same distance is `(m_(p)=1836 m_(e))`

Options

A. 2F
B. F
C. 1836 F
D. `F/(1836)`

Answer

To find the force of repulsion between two protons separated by the same distance as two electrons, we can use Coulomb's Law. Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Understanding Coulomb's Law**:
Coulomb's Law states that the force \( F \) between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \) is given by:
\[ F = k \frac{q_1 q_2}{r^2} \]
where \( k \) is Coulomb's constant.

2. **Force Between Two Electrons**:
For two electrons, each having a charge of \( -e \):
\[ F_e = k \frac{(-e)(-e)}{r^2} = k \frac{e^2}{r^2} \]
This is given as \( F \).

3. **Force Between Two Protons**:
For two protons, each having a charge of \( +e \):
\[ F_p = k \frac{(+e)(+e)}{r^2} = k \frac{e^2}{r^2} \]

4. **Comparing Forces**:
We see that:
\[ F_e = F_p = k \frac{e^2}{r^2} \]
Therefore, the force between two protons \( F_p \) is equal to the force between two electrons \( F_e \).

5. **Conclusion**:
Since both forces are equal, we conclude that the force between two protons separated by the same distance is also \( F \).

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

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