Explanation:

To solve this problem, we need to understand the relationship between the mass of the particles and the strength of the electrostatic force between them.

1. Mass of proton and electron:
It is given that the mass of a proton is nearly 1836 times more than the mass of an electron. This means that the mass of a proton (mp) is approximately 1836 times the mass of an electron (me).

2. Coulomb's law:
Coulomb's law states that the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

3. Coulomb force of repulsion between two protons:
If we have two protons separated by a finite distance, the electrostatic force between them will be given by Coulomb's law. Since both protons have the same charge, the force of repulsion between them will be proportional to the product of their charges, which can be written as e * e, where e is the charge of a single proton. Therefore, the force between the protons is Fe = ke * e / r^2, where ke is the electrostatic constant and r is the distance between the protons.

4. Electrostatic force between two electrons:
Similarly, if we have two electrons separated by the same distance, the electrostatic force between them will also be given by Coulomb's law. Since both electrons have the same charge, the force between them will be proportional to the product of their charges, which can be written as -e * -e, where -e is the charge of a single electron. However, the negative sign indicates that the force is attractive between the electrons. Therefore, the force between the electrons is Fe = -ke * e / r^2.

5. Comparison of forces:
Now, let's compare the forces between the protons and the electrons. The force between the protons is Fe = ke * e / r^2, and the force between the electrons is Fe = -ke * e / r^2.

Since the force between the electrons is attractive, it is opposite in direction to the force between the protons. Therefore, the magnitude of the force between the electrons is the same as the magnitude of the force between the protons, but with opposite sign.

6. Answer:
Hence, the electrostatic force between two electrons separated by the same distance is equal in magnitude to the electrostatic force of repulsion between two protons separated by the same distance. Therefore, the correct answer is option 'B' - the electrostatic force between two electrons separated by the same distance is equal to F.