Electrostatic Potential

Ratio of Electrostatic Forces: Protons vs. Electrons

We want to determine the ratio of the magnitudes of the electrostatic force between two protons at a distance to that between two electrons at the same distance .

Step 1: Coulomb's Law

Coulomb's Law states that the electrostatic force (F) between two point charges and separated by a distance is given by:

Where:

• is the magnitude of the electrostatic force.
• is Coulomb's constant ( ).
• and are the magnitudes of the charges.
• is the distance between the charges.

Step 2: Electrostatic Force between Two Protons

Let be the electrostatic force between two protons. The charge of a proton is , where .

Step 3: Electrostatic Force between Two Electrons

Let be the electrostatic force between two electrons. The charge of an electron is . Note that we're looking for the *magnitude* of the force, so we use the absolute value of the product of the charges.

Step 4: Calculate the Ratio

The ratio of the magnitudes of the electrostatic force between two protons to that between two electrons is:

Conclusion

The ratio of the magnitudes of the electrostatic force between two protons at a distance r apart to that between two electrons at the same distance of separation is 1:1.

A hollow sphere encloses an electric dipole (+q and -q charges).

Gauss's Law

Where is the net charge enclosed by the surface.

For a dipole:

Determine Electric Flux

Step 1: The electrostatic potential energy ( ) between two point charges and separated by distance is given by: Step 2: Since both charges are protons, we have:
Step 3: Since both charges are positive, they repel each other. As the distance between them decreases, decreases.
Step 4: Since , decreasing increases , meaning the electrostatic potential energy of the system increases.
Step 5: Therefore, the correct answer is (B). \bigskip