intrinsic vector formmagnetic flux densityPurpose - The purpose of this paper is to evaluate analytically the magnetic flux density and the magnetic vector potential produced by a linear current density or a li
where Ac is the area of the electric current loop and i is the current in the circuit. Magnetic flux density, B→, results in a torque on the moment which can lead to the moment aligning with the magnetic flux density. Hence, the magnetic moment, m→, can be defined as a vector rel...
Thus, we can consider that the magnetic flux density at each pixel in the blurred region is approximately determined by the vector from the nearest pixel on the object boundary to the pixel and by the electric current vector at the nearest pixel on the object edge. Using the Biôt-Savart ...
First, we will deal with a scalar 1D case and then we will extend our example to a general vectorial 3D case. In 1D, we only need thex-component of the magnetization, magnetic field, and magnetic flux. These will be represented with M, Hx, and Bx, respectively. We will also need t...
(6) B = ∇ × A (7) E = − dA − ∇V dt =-=(8)-=- where E = electric field intensity (Vm −1 ), B = magnetic flux density (Wbm −2 ), µ0 = permeability of free space (Hm −1 ), J = current density (Am −2 ), A = magnetic vector potential (Wbm...
ThePeriodic(boundary) condition allows for more general symmetry where both the current and the magnetic field vector can be at an angle to the boundary. The usage of this condition is limited to cases where the magnetic sources as well as the structure are periodic in space. Typically, the ...
, 1996]. Measurements of the twist of the emerging flux systems have shown that the change of the twist is rather small during the emergence [Wang and Abramenko, 1999]. In addition, photospheric measurements of the vector magnetic field have shown that the mean twist in active regions is ...
( 2.44 ). vector potential a , integrated vector potential \(\beta \) , and flux \(\phi \) are defined in ( 3.1 ) and ( 3.2 ). \(h^b\) is the schrödinger operator introduced in ( 3.7 ) \(\lambda ^b\) is the schrödinger operator introduced in ( 3.14 ). \(q_{\...
We at once note a complexity in our analogy of the electrostatic case; the differential charge element dq is a scalar quantity but the differential current element i ds is a vector quantity. One of the simplest problems in magnetism is that of a long straight wire carrying a current i. ...
Magnetic flux density: tesla (T) for SI; gauss (G) for CGS Another vector magnitude interesting in magnetic theory is magnetic field intensity, symbolized by H. It can be defined as the magnetic field created by a current circulating though a conductor but independently of the surrounding mater...