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Energy Associated With a Charge Distribution

Energy Associated With a Charge Distribution

The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

DC Battery

DC Battery

A conductor needs to be a component of a path that creates a closed loop or full circuit to have a continuous current flowing through it. A current starts to flow if an electric field is created inside an isolated conductor that is not part of a full circuit. The conductor quickly develops a net positive charge at one end and a net negative charge at the other. These charges generate an electric field opposite the direction of the applied electric field, which reduces the current. Eventually,...

Energy Stored in a Capacitor

Energy Stored in a Capacitor

When an archer pulls the string in a bow, he saves the work done in the form of elastic potential energy. When he releases the string, the potential energy is released as kinetic energy of the arrow. A capacitor works on the same principle in which the work done is saved as electric potential energy. The potential energy (UC) could be calculated by measuring the work done (W) to charge the capacitor.

Coulomb's Law and The Principle of Superposition

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Coulomb's Law describes the force experienced by two point charges under each other's presence. But what if there are more than two charges? For example, if there is a third charge, does it experience a force that is a simple combination of the individual forces due to the first two charges? Can it be described mathematically?
The Principle of Superposition answers the question. Yes, Coulomb's Law applies to each pair of charges, and the net force on each charge is the vector sum of...

Batteries and Fuel Cells

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A battery is a galvanic cell that is used as a source of electrical power for specific applications. Modern batteries exist in a multitude of forms to accommodate various applications, from tiny button batteries such as those that power wristwatches to the very large batteries used to supply backup energy to municipal power grids. Some batteries are designed for single-use applications and cannot be recharged (primary cells), while others are based on conveniently reversible cell reactions that...

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Related Experiment Video

Updated: Aug 26, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Entanglement, Coherence, and Extractable Work in Quantum Batteries.

Hai-Long Shi^1,2,3, Shu Ding¹, Qing-Kun Wan^2,3

¹School of Physics, Northwest University, Xi'an 710127, China.

Physical Review Letters

|October 7, 2022

Summary

Quantum batteries require quantum coherence and entanglement to generate extractable work. Coherence speeds up work extraction, while both coherence and entanglement influence the type and amount of work obtained.

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Area of Science:

Quantum Information Science
Quantum Thermodynamics
Quantum Energy Storage

Background:

Quantum batteries offer a novel approach to energy storage by leveraging quantum mechanical principles.
Understanding the fundamental resources enabling work extraction in quantum batteries is crucial for their development.

Purpose of the Study:

To investigate the role of quantum coherence and entanglement as resources for extractable work in quantum batteries.
To establish the relationship between these quantum resources and the characteristics of the extracted work.

Main Methods:

Theoretical analysis of quantum battery models, including central-spin, Tavis-Cummings, and spin-chain batteries.
Quantification of extractable work in relation to quantum coherence and battery-charger entanglement.
Comparison of work extraction speeds for coherent versus incoherent work.

Main Results:

Quantum coherence and/or battery-charger entanglement are necessary for generating nonzero extractable work during charging.
Coherence promotes coherent work extraction, while both coherence and entanglement can inhibit incoherent work extraction.
Achieving maximal coherent work is demonstrated to be faster than achieving maximal incoherent work.

Conclusions:

Quantum coherence and entanglement are essential resources that dictate the efficiency and nature of work extraction in quantum batteries.
The findings provide a theoretical framework for designing and optimizing quantum batteries for practical energy storage applications.