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Coulomb's Law is one of the fundamental principles in electrostatics. It quantifies the electrostatic force between two charges. Imagine you have two small charged spheres. The force between them depends on their charges and the distance separating them.
Coulomb's Law formula is:

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

- \( F \) is the force between the charges.- \( k \) is Coulomb’s constant, approximately \(8.99 \times 10^9 \text{ N m}^2\text{/C}^2\). - \( q_1 \) and \( q_2 \) are individual charges.- \( r \) is the distance between the charges.
Coulomb's Law tells us whether charged particles will attract or repel each other. Like charges repel, while opposite charges attract. This reflection in potential energy forms the basis for calculating the electrostatic potential energy using the formula \( U = \frac{k \cdot q_1 \cdot q_2}{r} \).
Understanding this principle helps to determine how charged spheres interact and respond when released on a frictionless track.

The principle of Conservation of Energy states that energy cannot be created or destroyed. Rather, it can only change from one form to another. When two charged spheres are released, the energy transformation is evident. Initially, all energy present is electrostatic potential energy. As the spheres move apart, this energy shifts into kinetic energy.
Here's how it works for our charged spheres:

• Initially, potential energy \( U_i = 35.96 \) J.
• As the spheres move infinitely apart, \( U_f = 0 \) J.

The initial potential energy converts entirely to kinetic energy. Thus:

• \( 2 \cdot \frac{1}{2} m v^2 = U_i \)

Each sphere acquires speed from the conversion of potential to kinetic energy. By applying the Conservation of Energy, students can understand the dynamics of motion for charged particles set in such a configuration.
Recognizing energy's unchanging nature in totality simplifies such calculations.

The Motion of Charged Particles is influenced by their interactions under electrostatic forces. With two positive charges, like in our example, the spheres repel each other. This repulsion results in both spheres moving away when released.
The principles guiding their motion include:

• Electrostatic repulsion due to like charges.
• Energy transformations, where potential energy transforms into kinetic energy.
• Frictionless surface allowing perfect energy conversion.

As charged particles accelerate apart, their velocity increases due to energy conservation. Both particles attain the same final speed of \( 8.48 \text{ m/s} \), calculated by:

• \( v = \sqrt{\frac{2 \times 35.96}{1.0}} \)

Through observing set examples, students gain insights into how charged particles behave under electrostatic conditions. The exercise highlights the predictable nature of electrostatic interactions and their resulting motion.