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Electrical Field in Materials
Published in Ahmad Shahid Khan, Saurabh Kumar Mukerji, Electromagnetic Fields, 2020
Ahmad Shahid Khan, Saurabh Kumar Mukerji
Current can also be classified as conduction, convection, and displacement current. The conduction current is the movement or flow of free electrons in a conductor due to an application of electric field. It is the ordered movement of electrons in the conductor. The convection current is the flow of charges (electrons and/or ions) in a fluid or in vacuum subjected to an electric field. Convection currents may also flow on conductor surfaces carrying distributions of free surface charges. Lastly, the displacement current; a quantity which first appeared in Maxwell’s equations, is defined in terms of the rate of change of electric displacement field (in a limited sense, also known as the field of electric flux density). It has an associated magnetic field just as actual currents do. It is not an electric current of moving charges but instead a time-varying electric field. In materials, there is also contribution toward the displacement current from the slight motion of bound charges or due to dielectric polarization caused by time-varying electric field.
Partial Differential Equations and Modelling
Published in Mattias Blennow, Mathematical Methods for Physics and Engineering, 2018
Problem 3.8. When studying electric fields in matter, it is often convenient to work in terms of the electric displacement fieldD→=ε0E→+P→, where P→ is the polarisation density. For weak external fields, the polarisation density can be assumed to depend linearly on the electric field and therefore () Pi=ε0χjiEj,
Permanent Magnet Motors and Halbach Arrays
Published in Ranjan Vepa, Electric Aircraft Dynamics, 2020
where the electric displacement field, D, the electric current density J, the magnetic flux density or magnetic flux per unit area B are related to the electric field E and the magnetic field strength H, by the material relations, D=εE, J=σE and B=μH where ε, σ and μ are the permittivity, the conductivity and the permeability, respectively, of the medium. The last relation may also be expressed as B=μH=μ0(μrH+M),
Acousto-optic coupling in 1-D phoxonic potential well nanobeam cavity using slow modes
Published in International Journal of Optomechatronics, 2023
Ying-Ping Tsai, Jyun-Jie Jhan, Bor‐Shyh Lin, Fu‐Li Hsiao
In formula (1), Q is the normalized displacement field, is the normal vector of the structure surface; E is the electric field, D is the electric displacement field, and the subscripts and denote the components parallel and perpendicular to the structure surface, respectively. Then take the volume integral of the inner product of the E field and D field in the AO cavity. represents the relative permittivity difference between the structural material and the surrounding medium, which is the difference between silicon and air in this paper, and is the reciprocal difference of relative permittivity. In formula (2), where n is the refractive index of silicon, is the photo-elastic tensor, and is the strain tensor generated by sound waves. Finally, is the zero-point momentum of the resonant structure, where is the reduced Planck constant, is the effective mass generated by the sound wave displacement field in the structure, and is the frequency of the sound wave.
Parabolic tapering piezoelectric rotational energy harvester: Numerical analysis with experimental validation
Published in Mechanics of Advanced Materials and Structures, 2023
Rakesh Ranjan Chand, Amit Tyagi
The piezoelectric constitutive equations under the outline of Euler-Bernoulli theory [27, 28], considering the host beam material as isotropic and homogeneous and using the tensor notations, can be given as; where and are the transverse electric displacement field and electric field along Z-direction. The stress and strain in the X-direction are and respectively. is the elastic stiffness constant (Young’s modulus), is the dielectric permittivity constant and is the stress constant for the piezoelectric material. In order to avoid confusion, Young’s modulus for the host beam and patch is symbolized as and respectively, in the following.
Finite-element analysis of scattering parameters of surface acoustic wave bandpass filter formed on barium titanate thin film
Published in International Journal of Smart and Nano Materials, 2018
Pavel E. Timoshenko, Valery V. Kalinchuk, Vladimir B. Shirokov
The finite-element modeling of piezoelectric material is well explained in [17–19]. The relation between the stress, strain, electric field, and electric displacement field in a stress-charge of a piezoelectric crystal is given by the piezoelectric linear constructive equations. They are governed by the continuum equation of motion, Maxwells equations under the quasi-static assumption, the strain-mechanical displacement relations and proper boundary conditions. In a homogeneous piezoelectric BT film, the stress component at each point depends on the applied electric field. The piezoelectric equations [20] in the time domain can be written in the following form: