Two particles with Q1=45 μC and Q2=85 μC are initially...

Two particles with $Q_{1}=45 \mu \mathrm{C}$ and $Q_{2}=85 \mu \mathrm{C}$ are initially separated by a distance of $2.5 \mathrm{m}$ and then brought closer together so that the final separation is $1.5 \mathrm{m}$. What is the change in the
electric potential energy?

Key Concepts

Electric Potential Energy

Electric potential energy in the context of electrostatics is the energy stored due to the positions of charged objects relative to one another. This energy is a function of the magnitudes of the charges and the distance between them, and it can be calculated using a formula derived from Coulomb’s law. It is a measure of the work done against the electrostatic force and plays a critical role in understanding the behavior of charged particles when their spatial configuration is altered.

Coulomb's Law

Coulomb's law describes the force between two point charges and is fundamental to understanding how charged particles interact. The law states that the electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle underlies the calculation of electric potential energy, as the potential energy is derived from the work required to bring charges from an infinite separation to a finite distance.

Distance Dependence in Electrostatic Interactions

The distance between charged particles is a crucial factor in both the electrostatic force and the electric potential energy they experience. When the separation between charges decreases, the potential energy increases in magnitude (becoming more positive or more negative depending on the sign of the charges). Any change in the distance results in a corresponding change in the potential energy, reflecting the work done in moving the charges through the electric field established by one another.

Work in Electrostatic Systems

In electrostatic systems, work is performed when changing the configuration of charged particles, and this work is directly related to the change in electric potential energy. Calculating the change in potential energy involves determining the difference in energy before and after a displacement of the charges. Understanding this concept is key to analyzing energy transformations and stability within systems of charges, which is essential in various applications of electromagnetism.

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