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Related Concept Videos

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...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
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...
Spherical and Cylindrical Capacitor01:26

Spherical and Cylindrical Capacitor

A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
Conventionally, considering the symmetry, the electric field between the concentric shells of a spherical capacitor is directed radially outward. The magnitude of the field, calculated by...
Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving01:23

Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

Consider a wooden box and a cylinder of known masses m1 and m2, respectively, hanging from a ceiling with the help of a massless pulley system.
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...

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Pool-Boiling Heat-Transfer Enhancement on Cylindrical Surfaces with Hybrid Wettable Patterns
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Published on: April 10, 2017

Coulomb problem on single- and double-wall cylinders.

Alexei Deinega1, Nina Voronova, Yurii Lozovik

  • 1Department of Physics, University of Toronto, 60 St George Street, Toronto, ON, M5S 1A7, Canada. deinega@physics.utoronto.ca

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|May 29, 2012
PubMed
Summary
This summary is machine-generated.

We calculated energies for charged particles on cylindrical surfaces. Excited state energies depend non-trivially on cylinder radius due to wavefunction symmetry, showing a crossover from 1D to 2D behavior.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Materials science

Background:

  • Confined quantum systems exhibit unique electronic properties.
  • Cylindrical geometries are relevant for nanoscale materials and devices.
  • Understanding charge carrier behavior is crucial for electronic applications.

Purpose of the Study:

  • To calculate ground and excited state energies of charge carriers on cylindrical surfaces.
  • To investigate the influence of cylinder radius and interwall distance on energy levels.
  • To analyze the transition from 1D to 2D quantum behavior.

Main Methods:

  • Solving the Schrödinger equation for confined charge carriers.
  • Utilizing symmetry properties of wavefunctions to explain energy level dependence.
  • Analyzing the impact of geometric parameters (radius, interwall distance) and mass ratios.

Main Results:

  • A non-trivial dependence of excited state energies on cylinder radius was found for single-wall cylinders.
  • The crossover from 1D to 2D behavior with increasing radius was detailed.
  • The ground state energy dependence on interwall distance and mass ratio was analyzed for double-wall cylinders.

Conclusions:

  • Wavefunction symmetry dictates the behavior of excited states in confined cylindrical systems.
  • Geometric parameters significantly influence the electronic properties of charge carriers.
  • This study provides insights into the quantum mechanics of confined charge carriers in novel geometries.