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Related Concept Videos

Electrostatic Boundary Conditions in Dielectrics01:27

Electrostatic Boundary Conditions in Dielectrics

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity.
Standing Waves in a Cavity01:28

Standing Waves in a Cavity

A household microwave and lasers are examples of standing electromagnetic waves in a cavity. When two conducting metal plates are placed parallel at the nodal planes, it creates a cavity where standing waves are formed. The cavity between the two planes is analogous to a stretched string held at the points x = 0 and x = L. Here, the distance 'L' between the two planes must be an integer multiple of half of the wavelength. The wavelengths that satisfy this condition are given by:
Dielectric Polarization in a Capacitor01:31

Dielectric Polarization in a Capacitor

The presence of a dielectric medium in a capacitor not only changes the voltage and capacitance but also affects the electric field. In general, dielectrics can be of two types: polar and nonpolar. In a polar dielectric, the positive and negative charges in the molecules are separated by a distance and hence have a permanent dipole moment. In contrast, no such charge separation exists in a nonpolar dielectric, however the nonpolar molecules get polarized in the presence of an external electric...
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...
Induced Electric Dipoles01:28

Induced Electric Dipoles

A permanent electric dipole orients itself along an external electric field. This rotation can be quantified by defining the potential energy because the external torque does work in rotating it. Then, the potential energy is minimum at the parallel configuration and maximum at the antiparallel configuration. While the former is a stable equilibrium, the latter is an unstable equilibrium.
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per...
Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

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 the problem,...

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The Preparation of Electrohydrodynamic Bridges from Polar Dielectric Liquids
10:03

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Published on: September 30, 2014

Electrodynamic Casimir effect in a medium-filled wedge.

Iver Brevik1, Simen A Ellingsen, Kimball A Milton

  • 1Department of Energy and Process Engineering, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. iver.h.brevik@ntnu.no

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2009
PubMed
Summary
This summary is machine-generated.

We studied the electrodynamic Casimir effect in a wedge, finding finite free energy results for specific dielectric media and cosmic string configurations. This research offers insights into quantum field theory in curved spacetimes.

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Area of Science:

  • Theoretical physics
  • Quantum field theory
  • Electrodynamics

Background:

  • The Casimir effect describes quantum vacuum fluctuations causing forces between objects.
  • Wedge-shaped geometries and cosmic strings present unique theoretical challenges in Casimir effect studies.
  • Previous research explored these effects in simpler geometries.

Purpose of the Study:

  • To re-examine the electrodynamic Casimir effect in a wedge geometry.
  • To investigate the influence of azimuthally symmetric materials on the effect.
  • To analyze radiation from a cosmic string's appearance in a wedge.

Main Methods:

  • Analysis of the Casimir effect in a wedge with perfect conductors and dihedral angle alpha=pi/p.
  • Modeling the wedge region with varying permittivity and permeability (epsilon1, micro1 and epsilon2, micro2).
  • Comparison with circular-cylindrical geometries and consideration of noninteger azimuthal quantum numbers (mp).

Main Results:

  • Obtained finite results for free energy under specific conditions, including periodic boundary conditions and dispersion.
  • Found finite results for changes in 'a' with constant speed of light inside and outside radius 'a'.
  • Derived finite results for weak coupling in purely dielectric media and analyzed cosmic string radiation.

Conclusions:

  • The study provides finite results for the Casimir effect in a wedge, overcoming zero-mode divergences.
  • The findings are analogous to cosmic string systems and offer insights into quantum field theory.
  • The research contributes to understanding vacuum energy and radiation in complex geometries.