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The Conservation of Energy principle is a fundamental concept in physics stating that energy cannot be created or destroyed; it can only change form. In the context of electrostatics, this principle is particularly important. When dealing with charged particles, such as the ones in the given problem, energy transformation occurs between kinetic energy and electric potential energy.
This principle helps us to understand and calculate how the moving charge's kinetic energy is converted into electric potential energy as it moves closer to the fixed charge. As the particle travels toward the fixed charge, its speed (kinetic energy) decreases because of the repulsive force acting upon it. When its speed reaches zero, the initial kinetic energy of the particle is fully transformed into electric potential energy.

• Initial kinetic energy = final electric potential energy
• No external work is done; only energy transformation occurs within the system

The formula used in the problem relied heavily on the conservation of energy. Specifically, it transformed initial kinetic energy into electric potential energy to determine the stopping distance.

Electric potential energy is the energy stored in a system of charged particles due to their positions. In the situation described by the exercise, electric potential energy plays a crucial role as the particle with charge decimalsub -8.00 \mu Ccomes under the influence of the fixed charge of decimalsub -3.00 \mu C.
The concept can be understood by recognizing that like charges repel each other. As our particle approaches the fixed charge, it experiences a force that does work. This work is converted into electric potential energy. Therefore, as the particle progresses, its kinetic energy decreases while its electric potential energy increases.
The equation representing electric potential energy for two point charges is:\[ PE = k \frac{q_1 q_2}{r} \] where:

• k: Coulomb's constant
• q_1, q_2: the magnitudes of the two charges
• r: the distance between the charges

This formula is used in the problem to calculate the conversion of the particle's initial kinetic energy into potential energy, ultimately allowing us to find out at what point the particle's motion stops.

Kinetic energy is the energy that a body possesses due to its motion. In simpler terms, it is the energy of movement. The given problem starts by considering the kinetic energy of the moving particle at its initial speed of 65.0 m/s.
The equation used to compute kinetic energy is:\[ KE = \frac{1}{2} mv^2 \] Where:

• m: mass of the particle which is decimalsub 7.20 \times 10^{-3} \textrm{ kg}
• v: initial speed of the particle

As the particle moves towards the fixed charge, its initial kinetic energy is converted gradually into electric potential energy due to the forces acting against its motion. When all the kinetic energy has been converted, the particle comes to a stop—a key point to solve the exercise.
By understanding how kinetic energy diminishes as the particle approaches the fixed charge, we are able to determine how far it travels before its velocity, or speed, becomes zero. This information is crucial for completing the steps to the solution.

Coulomb's Law describes the electrostatic interaction between two charged objects. It essentially tells us how strong the force is between charges based on their magnitudes and the distance separating them. For the exercise at hand, Coulomb's Law explains the repulsive force that causes the particle to decelerate as it approaches the fixed charge.
The fundamental equation of Coulomb's Law is:\[ F = k \frac{|q_1 q_2|}{r^2} \] where:

• F: the magnitude of the force between the two charges
• k: Coulomb's constant (decimalsub 8.99 \times 10^9 \textrm{ N m}^2/\textrm{C}^2)
• q_1, q_2: the charges
• r: the distance between the centers of the two charges

In the specific exercise, Coulomb's Law is used to understand why the kinetic energy of the particle decreases—the repulsive force between the two negatively charged particles is explained by this fundamental law. Understanding this force is essential to comprehend how the transition of energy occurs, allowing us to calculate the stopping distance of the moving charge.