An electron is projected with an initial speed vi=3.2 ×10^5 m / s directly toward a very distant

step 1 this question, we have an electron that moves toward a proton, okay? If a speed, initial speed o

An electron is projected with an initial speed vi=3.2 ×10^5...

An electron is projected with an initial speed $v_{i}=3.2 \times 10^{5} \mathrm{m} / \mathrm{s}$ directly toward a very distant proton that is at rest. Because the proton mass is large relative to the electron mass, assume that the proton remains at rest. By calculating the work done on the electron by the electrostatic force, determine the distance between the two particles when the electron instantaneously has speed 2$v_{i .}$

An electron is projected with an initial speed $v_{i}=3.2 \times 10^{5} \mathrm{m} / \mathrm{s}$ directly toward a very distant proton that is at rest. Because the
proton mass is large relative to the electron mass, assume that the
proton remains at rest. By calculating the work done on the electron by the electrostatic force, determine the distance between the
two particles when the electron instantaneously has speed 2$v_{i .}$

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Key Concepts

Coulomb's Law

This concept describes the force between two charged particles, stating that the electrostatic force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. It provides the fundamental relation needed to determine how the force changes as the distance between the electron and proton changes.

Electrostatic Potential Energy

This refers to the energy stored between two charges due to their positions in an electric field. For a pair of point charges, it is computed using a formula that involves the product of the charges and the inverse of the separation distance, offering a way to relate distance and energy in electrostatic systems.

Work-Energy Theorem

This theorem states that the work done on an object by the net force acting on it is equal to its change in kinetic energy. In the context of an electron moving in the electric field of a proton, calculating the work done by the electrostatic force allows one to connect the change in speed (and thus kinetic energy) with the change in potential energy as the distance between the particles varies.

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