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Understanding how forces act between charged particles is essential in physics. Coulomb's Law serves as the foundation for electrostatics and provides the means to calculate forces between two point charges. The equation is formulated as follows:\[F = \frac{k \cdot |q_1 \cdot q_2|}{r^2}\]where:- \( F \) represents the electrostatic force between the charges.- \( k \) is Coulomb's constant, with a value of approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \).- \( q_1 \) and \( q_2 \) are the magnitudes of the charges involved.- \( r \) is the distance separating the charges.The inverse square relationship in Coulomb's Law means that as the distance \( r \) increases, the force \( F \) decreases. This is crucial when considering how charged particles behave over varying distances.

Protons, being fundamental charged particles, have a known mass and charge that allow us to predict their motion under specific forces. In this scenario, once a proton is released, it is only subjected to the electrostatic force by the fixed proton. To determine its initial acceleration, Newton's Second Law comes into play:\[a = \frac{F}{m}\]Here \( F \) is the force calculated using Coulomb’s Law, and \( m \) is the mass of a proton, \( 1.67 \times 10^{-27} \, \text{kg} \). By substituting the electrostatic force value, we calculate the initial acceleration. This initial acceleration will decrease over time as the proton moves away, reducing the electrostatic attraction.

Newton's Second Law is one of the cornerstones of classical mechanics, providing a quantitative description of the motion of objects. It is expressed as:\[F = m \cdot a\]where:- \( F \) is the net force on the object.- \( m \) is the mass of the object.- \( a \) is the acceleration of the object.In the context of the proton problem, this law tells us that the acceleration of an object (or proton, in this case) is directly proportional to the net force acting on it and inversely proportional to the object’s mass. As the proton is released, the electrostatic force provides the net force, and using the mass of the proton, we calculate its acceleration. This force decreases as the proton moves further away from the fixed proton, which affects its acceleration over time. Thus, Newton's Second Law not only aids us in computational calculations but also deepens our understanding of how forces and motion are interrelated.