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Related Concept Videos

Toroids01:27

Toroids

A toroid is a closely wound donut-shaped coil constructed using a single conducting wire. In general, it is assumed that a toriod consists of multiple circular loops perpendicular to its axis.
When connected to a supply, the magnetic field generated in the toroid has field lines circular and concentric to its axis. Conventionally, the direction of this magnetic field is expressed using the right-hand rule. If the fingers of the right hand curl in the current direction, the thumb points in the...
Torque On A Current Loop In A Magnetic Field01:13

Torque On A Current Loop In A Magnetic Field

The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop...
Torque01:10

Torque

Torque is an important quantity for describing the dynamics of a rotating rigid body. We see the application of torque in many ways in the world, such as when pressing the accelerator in a car, which causes the engine to apply additional torque on the drivetrain. Here, we define torque and provide a framework to create an equation to calculate torque for a rigid body with fixed-axis rotation.
Torque can be considered as the rotational counterpart to force. Since forces change the translational...
Force On A Current Loop In A Magnetic Field01:17

Force On A Current Loop In A Magnetic Field

Magnetic forces on wires carrying current are most frequently applied in motors. A DC motor is a device that converts electrical energy into mechanical work. In motors, wire loops are enclosed in a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate. The direction of the current is reversed once the loop's surface area is lined up with the magnetic field, causing a constant torque on the loop. During the process, commutators...
Magnetic Field Of A Current Loop01:16

Magnetic Field Of A Current Loop

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the loop can be calculated using the Biot-Savart law.
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...

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Demonstration of Spin-Multiplexed and Direction-Multiplexed All-Dielectric Visible Metaholograms
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Published on: September 25, 2020

Invisibility cloaks for toroids.

Yu You1, George W Kattawar, Ping Yang

  • 1Department of Physics and Institute for Quantum Studies, Texas A&M University, College Station, TX 77843, USA. youyu@tamu.edu

Optics Express
|April 15, 2009
PubMed
Summary
This summary is machine-generated.

Researchers derived material properties for toroidal invisibility cloaks using coordinate transformation. Simulations confirmed cloaking effects, extending electromagnetic cloaking to complex shapes.

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Area of Science:

  • Electromagnetism and materials science
  • Metamaterials research

Background:

  • Coordinate transformation is a key method for designing transformation electromagnetics devices.
  • Previous invisibility cloaks primarily focused on spherical or 2D cylindrical geometries.

Purpose of the Study:

  • To derive the material properties for toroidal invisibility cloaks.
  • To investigate the feasibility of cloaking complex, arbitrarily-shaped objects.

Main Methods:

  • Utilized the coordinate transformation method to determine permittivity and permeability tensors.
  • Employed the generalized discrete-dipole approximation (DDA) method for electromagnetic simulations.

Main Results:

  • Toroidal cloak properties differ significantly from spherical cloaks but resemble 2D cylindrical cloaks due to inner boundary singularities.
  • Simulations validated the cloaking effect through electric field distribution analysis.

Conclusions:

  • The study successfully derived the necessary material properties for toroidal invisibility cloaks.
  • This work advances electromagnetic cloaking by enabling its application to complex geometries beyond simple shapes.