91Ó°ÊÓ

Coulomb's Law is a fundamental principle in physics that helps us understand the electrostatic interaction between two charged particles. It states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. This can be represented mathematically as:

• F = \( \frac{k \, |q_1 \, q_2|}{r^2} \)

where:

• \( F \) is the force between the charges,
• \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
• \( r \) is the separation between the charges,
• \( k = 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \) is Coulomb's constant.

Coulomb's Law is pivotal in calculating the electrostatic potential energy between charged particles. In our exercise, we applied Coulomb's Law to determine the potential energy difference when two protons are moved closer.
Understanding this law lays the groundwork for exploring how charged particles interact, as seen with protons that carry equal positive charges.

Protons are subatomic particles with a positive charge, commonly found in the nuclei of atoms. When discussing proton interactions, it is crucial to consider their electrostatic repulsion due to like charges.
In the exercise, we analyzed how the potential energy changes when two protons are moved from an atomic distance to a nuclear distance.
Given their identical positive charges, protons repel each other, and overcoming this force requires work input.
As the distance decreases:

• The potential energy increases because the repulsive force grows stronger.
• This increase in potential energy results from the electrical force exerted by each proton on the other.

These interactions are essential for understanding nuclear forces. Despite the repulsion, protons can still coexist in atomic nuclei due to the presence of the nuclear force, which is not covered in this specific problem.

Kinetic energy conversion involves the transformation of potential energy into kinetic energy and vice versa.
In part (b) of the exercise, we dealt with the conversion of electrostatic potential energy into kinetic energy for two protons.
Initially, the protons are held close together, resulting in a high potential energy. Once they are released:

• The potential energy decreases as they move back to their original separation.
• The lost potential energy is converted into kinetic energy, giving the protons speed.

We computed how fast the protons travel by equating the change in potential energy to kinetic energy using the formula:

• \( \Delta U = K_f = \frac{1}{2} m v^2 \)

where:

• \( \Delta U \) is the change in potential energy,
• \( K_f \) is the final kinetic energy,
• \( m \) is the mass of a proton,
• \( v \) is the velocity of the protons.

By calculating this conversion, we highlight the intricate dance of forces and energy that governs particle motion at microscopic scales.