Magnetic field
From the university physics course it is well known that magnetic field is just one side of the electromagnetic field.
The theory of the electromagnetic field is based on Maxwell's equations. They can be significantly simplified by assuming that the
magnetic field quantities are solely determined by the instantaneous values of source currents and that the time variations of the
magnetic fields follow directly from the variations of the sources. It can be said simply that when a current flows it creates magnetic field.
An opposite statement is also valid  if a magnetic field is observed, there is a current responsible for that field creation. Magnetic field is basically characterized by two vector quantities:
B  magnetic flux density.
Both of these quantities are specified for a given space point. Magnetic flux density B is associated with the mechanical
force which a current carrying element exerts in that same point. B is measured in teslas [T], 1T = 1 V.s/m^{2}
and strongly depends on the magnetic properties of the material penetrated by an external magnetic field. The magnetic field intensity H
is measured in A/m m and depends only on the currents creating the field and geometry factors. As M for isotropic materials is usually proportional to H (M = xH): where _{r} = (l+x) is called relative magnetic permeability of the material concerned. An additional and very important quantity associated with the magnetic field is the magnetic flux . It is defined as = B.S, where S is introduced as a certain surface in space, as for example depicted in figure: It should be noted that in case the distribution of B over the surface S is not uniform, than actually a surface integral shall be created to find the flux : Here ds is the surface element vector. It is clear now from the dot product B.ds that the flux is actually scalar quantity. Nevertheless in engineering it is convenient that the flux has the same as B direction (it is said to flow in that same direction). In practical engineering when the conductor, creating the loop to form the surface S as depicted in figure, is not a single one but has many turns, an additional important quantity is introduced  the flux linkage : Here w is the number of the turns. Such configuration is named in engineering a coil (winding). The flux linkage is used mainly, when we apply the Faraday's law of electromagnetic induction (when a voltage is induced in a coil by a timevarying magnetic field). The flux linkage is also important when the magnetic energy stored in a winding is calculated. It helps to introduce the winding inductance L. 

ELECTROMAGNETIC FIELD COMPUTATION AND MODELLING : UNIT I INTRODUCTION Review of basic field theory  electric and magnetic fields  Maxwell's equations  Laplace, Poisson and Helmoltz equations  principle of energy conversion  force/torque calculation  Electro thermal formulation. UNIT II SOLUTION OF FIELD EQUATIONS Limitations of the conventional design procedure, need for the field analysis based design, problem definition , solution by analytical methodsdirect integration method  variable separable method  method of images, solution by numerical methods Finite Difference Method. UNIT III SOLUTION OF FIELD EQUATIONS II Finite element method (FEM)  Differential/integral functions  Variational method  Energy minimization  Discretisation  Shape functions Stiffness matrix 1D and 2D planar and axial symmetry problem. UNIT IV FIELD COMPUTATION FOR BASIC CONFIGURATIONS Computation of electric and magnetic field intensities Capacitance and Inductance  Force, Torque, Energy for basic configurations. UNIT V DESIGN APPLICATIONS Insulators Bushings  Cylindrical magnetic actuators  Transformers  Rotating machines. REFERENCES : 1. K.J.Binns, P.J.Lawrenson, C.W Trowbridge, "The analytical and numerical solution of Electric and magnetic fields", John Wiley & Sons, 1993. 2. Nathan Ida, Joao P.A.Bastos , "Electromagnetics and calculation of fields", SpringerVerlage, 1992. 3. Nicola Biyanchi , "Electrical Machine analysis using Finite Elements", Taylor and Francis Group, CRC Publishers, 2005. 4. S.J Salon, "Finite Element Analysis of Electrical Machines." Kluwer Academic Publishers, London, 1995, distributed by TBH Publishers & Distributors, Chennai, India. 5. User manuals of MAGNET, MAXWELL & ANSYS software. 6. Silvester and Ferrari, "Finite Elements for Electrical Engineers" Cambridge University press, 1983. Electromagnetic Module. Modelling, Analysis and Design. 
Physical Process Modeling Resources: Mathematics Physics Electronics Programming Heat transfer 