Calculation of electromagnetic properties of regular and random arrays of metallic and dielectric cylinders

R C McPhedran1, L C Botten, A A Asatryan

  • 1School of Physics, University of Sydney, NSW 2006, Australia.

Related Concept Videos

Gauss's Law: Problem-Solving01:10

Gauss's Law: Problem-Solving

Gauss's law helps determine electric fields even though the law is not directly about electric fields but electric flux. In situations with certain symmetries (spherical, cylindrical, or planar) in the charge distribution, the electric field can be deduced based on the knowledge of the electric flux. In these systems, we can find a Gaussian surface S over which the electric field has a constant magnitude. Furthermore, suppose the electric field is parallel (or antiparallel) to the area vector...
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,...
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...
Electromagnetic Waves in Matter01:30

Electromagnetic Waves in Matter

Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, or glass.
Consider the electromagnetic wave passing through a dielectric medium. In such a case, Maxwell's equations get modified. In Ampere's law, ε0 , the dielectric permittivity of free space is replaced with ε, the permittivity of dielectric. Also, the vacuum permeability μ0 is replaced by the permeability of the medium, μ.
Furthermore, the...
Electric Field of a Charged Disk01:23

Electric Field of a Charged Disk

The simplest case of a surface charge distribution is the uniformly charged disk. Calculating its electric field also helps us calculate the electric field of a large plane of charge.
The system's symmetry is in the cylindrical directions across the plane of the charge. As a result, the electric fields created by various surface charge elements nullify each other in the direction parallel to the surface. Thereby, the resulting electric field is perpendicular to the plane. Since the disk is...
Inductance: Solid Cylindrical Conductor01:24

Inductance: Solid Cylindrical Conductor

To calculate the inductance of a solid cylindrical conductor, consider a 1-meter section of a non-magnetic, current-carrying conductor with radius r. Disregarding end effects and assuming uniform current density, Ampere's law helps determine the magnetic field inside the conductor. This law states that the magnetic field intensity H is concentric and constant within the conductor.
Given the uniform current distribution, the magnetic field Hx and flux density Bx inside the conductor are...