A Proof of the Biot-Savart Law

1968 ◽  
Vol 72 (689) ◽  
pp. 437
Author(s):  
B. G. Newman
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Electromagnetic Field ◽  
Fluid Mechanics ◽  
Small Length ◽  
Line Vortex ◽  
Line Current ◽  
Electromagnetic Field Theory ◽  
The Magnetic Field

The Biot-Savart law gives the velocity associated with an elemental portion of line vortex, or the magnetic field associated with an elemental portion of line current. The following proof may appeal to students who approach fluid mechanics or electromagnetic-field theory from the engineering viewpoint. It will be stated in terms of fluid mechanics. Consider a very small length δs of line vortex of circulation strength Γ. At P(x) the velocity δV associated with this portion depends on Γ δs and x.

The eigenvalues of electromagnetic angular momentum

1936 ◽  
Vol 32 (4) ◽  
pp. 614-621 ◽  
Author(s):  
M. H. L. Pryce
Keyword(s):  
Magnetic Field ◽  
Field Theory ◽  
Electromagnetic Field ◽  
Angular Momentum ◽  
Vector Potential ◽  
Charged Particles ◽  
Radial Component ◽  
Spin Angular Momentum ◽  
The Magnetic Field ◽  
Field Strengths

It is shown that the eigenvalues of the angular momentum of the electromagnetic field containing a number of charged particles, apart from spin angular momentum, are only the integral multiples of ħ. This is shown by using cylindrical polar variables, and taking a particular choice of the vector potential in which the radial component is zero, defined explicitly in terms of the magnetic field strengths. By expanding in terms of the Fourier functions einθ, the angular momentum is separated out into terms independent of one another, each taking on only integral values in units of ħ.The arguments all apply equally well to a modified field theory such as that of Born and Infeld.

Investigating flexible textile-based coils for wireless charging wearable electronics

2019 ◽  
Vol 50 (3) ◽  
pp. 333-345 ◽  
Author(s):  
Danmei Sun ◽  
Meixuan Chen ◽  
Symon Podilchak ◽  
Apostolos Georgiadis ◽  
Qassim S Abdullahi ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Electrical Conductivity ◽  
Electromagnetic Field ◽  
Electric Field ◽  
Dimensional Stability ◽  
Screen Printing ◽  
Wearable Electronics ◽  
Wireless Charging ◽  
The Magnetic Field ◽  
Screen Printed

Smart and interactive textiles have been attracted great attention in recent years. This research explored three different techniques and processes in developing textile-based conductive coils that are able to embed in a garment layer. Coils made through embroidery and screen printing have good dimensional stability, although the resistance of screen printed coil is too high due to the low conductivity of the print ink. Laser cut coil provided the best electrical conductivity; however, the disadvantage of this method is that it is very difficult to keep the completed coil to the predetermined shape and dimension. The tested results show that an electromagnetic field has been generated between the textile-based conductive coil and an external coil that is directly powered by electricity. The magnetic field and electric field worked simultaneously to complete the wireless charging process.

Increasing the effective affect of the magnetic field on the weld pool

2021 ◽  
pp. 29-33
Author(s):  
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Magnetic Fields ◽  
Weld Pool ◽  
Electromagnetic Effects ◽  
Weld Pools ◽  
The Magnetic Field

Variants of weld pools obtained by verification with the influence of magnetic fields are considered. Methods for increasing the effectiveness of electromagnetic effects during welding are proposed. Keywords: welding, electromagnetic field, weld pool, induction, coating. [email protected], [email protected]

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