A point charge q1 is held stationary at the origin. A second...

A point charge $q_{1}$ is held stationary at the origin. A second charge $q_{2}$ is placed at point $a$, and the electric potential energy of the pair of charges is $+5.4 \times 10^{-8} \mathrm{~J}$. When the second charge is moved to point $b,$ the clectric force on the charge does $-1.9 \times 10^{-8} \mathrm{~J}$ of work. What is the electric potential energy of the pair of charges when the second charge is at point $b ?$

Key Concepts

Electric Potential Energy

This is the energy stored in a system due to the positions of charged particles relative to one another. It depends on the magnitude of the charges and the distance between them as described by Coulomb's law, and it represents the potential for the system to do work due to electrostatic interactions.

Work Done by Conservative Forces

In electrostatics, the electric force is a conservative force, meaning that the work done by this force when moving a charge between two points is independent of the path taken. The change in electric potential energy of the system is equal to the negative of the work done by the electric force, providing a key link between energy changes and work in the system.

Point Charge Interactions

Interactions between point charges are governed by Coulomb's law, which defines the force between two charges as directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Understanding these interactions is crucial to calculating the potential energy and analyzing the work done when charges are moved in the field.

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