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The concept of the conservation of energy is all about understanding that energy cannot just disappear or appear out of nowhere. Instead, it can only change forms or transfer from one system to another. In the context of our problem, we are dealing with electric potential energy, which is the energy stored in the positions of charged particles.
When the second charge moves from point \(a\) to point \(b\), the conservation of energy tells us that the total energy before and after the charge's movement remains the same. The initial electric potential energy and the work done by the electric force are all part of this energy balance.
In our scenario, as the charge \(q_2\) moves from point \(a\) to point \(b\), the work done on the charge by the electric force changes the system's electric potential energy. It's crucial to consider this very principle in calculations, as it ensures that all forms of energy are conserved across the transformation.

The work-energy principle explains how work done by forces results in a change in energy. Simply put, work can modify the energy state of a system.
In our problem, this principle is evident when the electric force does work on the charge \(q_2\) as it moves from point \(a\) to point \(b\). The work done has been given as \(-1.9 \times 10^{-8} \mathrm{~J}\).
This principle allows us to understand that:

• The amount of work done is equivalent to the change in electric potential energy.
• This change in energy determines how the electric potential energy at point \(b\) will differ from the initial state at point \(a\).

By applying the work-energy principle, we recognize that any work performed (negative or positive) directly translates to a change in the system's energy.

An electric force is a fundamental interaction between charges, and it can do work on charges, causing changes in their energy states. Electric force is central to this problem since it brings about the movement of the charge \(q_2\) and helps us determine the final electric potential energy.
The electric force can exert a push or pull on the charge, depending on the nature of the charges involved. Importantly, it has the ability to do work as the charge moves, influencing the potential energy of the system.
As given in the problem, the work done by this force is negative, \(-1.9 \times 10^{-8} \mathrm{~J}\), which signifies that energy is released by the electric field. The negative sign suggests that the energy of the system decreases in that direction or is transferred elsewhere. This interaction is what leads to the change in potential energy that we calculated using the conservation of energy and work-energy principle.