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Coulomb's Law01:30

Coulomb's Law

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them. The direction of the force vector is along the imaginary line joining the two objects and is dictated by the signs of the charges involved.
Newton's third law applies to the Coulomb force — the force on...
Coulomb's Law and The Principle of Superposition01:15

Coulomb's Law and The Principle of Superposition

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 the...
Comparison Between Electrical And Gravitational Forces01:24

Comparison Between Electrical And Gravitational Forces

There are four fundamental forces in nature: the gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force. To compare the numerical strengths of the first two, take two particles of the same kind. Since electrons are fundamental particles, they are a good example.
Since both are inverse square law forces, the distance gets canceled when the ratio of the two forces is considered. Instead, the ratio of the electrical and gravitational forces depends on...
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
Van der Waals Interactions01:24

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.Polar molecules have a partial positive charge on one end and a partial negative charge on the other end of the molecule,...

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Related Experiment Video

Updated: Jul 13, 2026

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing
15:58

Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

Published on: December 3, 2013

Coulomb interactions in Ga LMIS.

Tomás Radlicka1, Bohumila Lencová

  • 1Institute of Scientific Instruments AS CR, Královopolská 147, Brno, Czech Republic. radlicka@isibrno.cz

Ultramicroscopy
|August 19, 2007
PubMed
Summary

Low emission currents from gallium liquid-metal ion sources (LMIS) create bright ion beams, but Coulomb interactions limit performance. This study models these interactions to improve understanding and estimation of LMIS tip size.

Area of Science:

  • Physics
  • Materials Science
  • Nanotechnology

Background:

  • Liquid-metal ion sources (LMIS) are crucial for generating fine ion beams.
  • Coulomb particle-particle interactions significantly limit beam brightness in LMIS.
  • Understanding these interactions is key to optimizing ion beam performance.

Purpose of the Study:

  • To computationally investigate the impact of Coulomb interactions on ion beam properties.
  • To analyze energy spread, virtual crossover size, and beam brightness.
  • To develop a method for estimating LMIS tip size using experimental data.

Main Methods:

  • Numerical integration of the equation of motion for ion beam evolution.
  • Simulation of ion beam dynamics considering Coulomb interactions.

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Last Updated: Jul 13, 2026

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Measurement of Coherence Decay in GaMnAs Using Femtosecond Four-wave Mixing

Published on: December 3, 2013

High-Sensitivity Nuclear Magnetic Resonance at Giga-Pascal Pressures: A New Tool for Probing Electronic and Chemical Properties of Condensed Matter under Extreme Conditions
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High-Sensitivity Nuclear Magnetic Resonance at Giga-Pascal Pressures: A New Tool for Probing Electronic and Chemical Properties of Condensed Matter under Extreme Conditions

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  • Comparison of computational results with experimental data.
  • Main Results:

    • Computations reveal the influence of emission tip dimensions on beam characteristics.
    • The study quantifies the limitations imposed by Coulomb interactions.
    • A correlation between simulation outcomes and experimental measurements was established.

    Conclusions:

    • Coulomb interactions are a primary factor limiting ion beam quality from LMIS at low currents.
    • Numerical modeling provides valuable insights into ion beam physics.
    • The developed approach enables more accurate estimation of LMIS tip size.