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Continuous Charge Distributions01:17

Continuous Charge Distributions

7.4K
Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
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RC Circuits: Charging A Capacitor01:30

RC Circuits: Charging A Capacitor

4.0K
A circuit containing resistance and capacitance is called an RC circuit. A capacitor is an electrical component that stores electric charge by storing energy in an electric field. Consider a simple RC circuit having a DC (direct current) voltage source ε, a resistor R, a capacitor C, and a two-way position switch. In the circuit, the capacitor can be charged or discharged depending on the position of the switch.
When the switch is moved to connect the battery, the circuit reduces to a simple...
4.0K
RC Circuit with Source01:15

RC Circuit with Source

1.7K
When a DC source is abruptly applied to an RC (Resistor-Capacitor) circuit, the voltage can be represented as a unit step function. The voltage across the capacitor, known as the step response, characterizes how the circuit reacts to this sudden change in input.
Due to the inherent properties of a capacitor, its voltage cannot change instantaneously. This means that immediately after the switch is closed, the capacitor's voltage remains the same as it was just before the switch was closed.
1.7K
Charging Conductors By Induction01:15

Charging Conductors By Induction

8.4K
The Earth is a good conductor of electricity, and it is so big that it can be considered an infinite source or sink of charges. It can easily exchange charges with any matter.
Generally, conductors like metals do not allow any excess charge to be present on them. Any excess charge added to metals easily flows away, for example, when a metal is placed on the Earth. This process is called earthing.
However, conductors can be charged by a process called induction. For example, consider charging a...
8.4K
Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

810
A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of...
810
Series RLC Circuit with Source01:12

Series RLC Circuit with Source

567
Consider the operation of an automobile ignition system, a crucial component responsible for generating a spark by producing high voltage from the battery. This system can be described as a simple series RLC circuit, allowing for an in-depth analysis of its complete response.
In this context, the input DC voltage serves as a forcing step function, resulting in a forced step response that mirrors the characteristics of the input. Applying Kirchhoff's voltage law to the circuit yields a...
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Related Experiment Video

Updated: Oct 4, 2025

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

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Accelerated simulation method for charge regulation effects.

Tine Curk1, Jiaxing Yuan2, Erik Luijten1

  • 1Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, USA.

The Journal of Chemical Physics
|February 2, 2022
PubMed
Summary
This summary is machine-generated.

We developed an efficient charge regulation Monte Carlo (CR-MC) method to accurately simulate how charges change dynamically on molecules and nanoparticles. This new hybrid simulation method allows for more realistic modeling of complex systems with many charged sites.

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Area of Science:

  • Computational chemistry
  • Physical chemistry
  • Biophysics

Background:

  • The net charge of solvated entities is crucial for their behavior.
  • Charge regulation (CR) describes how local charge depends on ionizable groups.
  • Current models often approximate CR with constant net charges, limiting accuracy.

Purpose of the Study:

  • To introduce an efficient charge regulation Monte Carlo (CR-MC) method.
  • To integrate CR-MC with molecular dynamics (MD) for hybrid simulations.
  • To enable accurate modeling of systems with dynamic charge distributions.

Main Methods:

  • Developed a novel CR-MC algorithm for explicit charge redistribution.
  • Implemented CR-MC within the AMMP (Atomic/Molecular Massively Parallel Simulator) package.
  • Created a hybrid MD/CR-MC simulation approach for implicit-solvent systems.

Main Results:

  • The CR-MC method accurately samples grand-canonical charge distributions.
  • Computational cost scales linearly with ionizable groups, enabling large systems.
  • Demonstrated CR-MC's ability to simulate polyelectrolyte transitions and nanoparticle interactions.

Conclusions:

  • The hybrid MD/CR-MC method provides an efficient and accurate way to model charge regulation.
  • This approach overcomes limitations of constant-charge approximations.
  • Enables detailed study of phenomena influenced by dynamic charge distributions.