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Mag­neto­stat­ics is the study of the Mag­net­ic Field pro­duced by stead­ily mov­ing elec­tric charges. In addi­tion to Elec­tro­stat­ics, Mag­neto­stat­ics is part of the found­a­tion or build­ing blocks upon which the the­ory of Elec­tro­dynam­ics is built. The cen­ter of Mag­neto­stat­ics is cal­cu­lat­ing the Mag­net­ic Field pro­duced by stead­ily mov­ing accu­mu­la­tions of charge. There­after, one can ana­lyse the mag­neto­stat­ic force on charged particles. This is basic­ally the applic­a­tion of the law of Biot and Sav­art. How­ever, just like life, things are not quite that simple. Just like the study of Coulomb’s Law, the math­em­at­ics is quite cum­ber­some due to the vec­tor nature of the Mag­net­ic Field and its non zero curl. There­fore, the study of Mag­neto­stat­ics is really about defin­ing a vec­tor mag­net­ic poten­tial ‘A’ and using this poten­tial in order to eval­u­ate the field and the force it pro­duces. Much time and effort is devoted to the mag­net­ic poten­tial and apply­ing a power series expan­sion to it. (As an import­ant aside; I have found that tra­di­tion­al lec­ture courses gloss over the the­ory sur­round­ing the scal­ar [and later vec­tor] poten­tials. This is prob­ably for good reas­on as the Helm­holtz The­or­em is pretty tedi­ous Vec­tor Cal­cu­lus. None the less, I attempt to derive almost all terms/theorems/quantities which I use. See my Vec­tor Cal­cu­lus for Elec­tro­mag­net­ism video tutori­al series for more.)

Return to Elec­tro­mag­net­ism and Optics

Video # Video Tutori­al Title Remarks
1 Lorentz Force Law Describes the elec­tro­stat­ic force between charged particles
2 Cur­rent Dens­ity and the Con­tinu­ity Equation Volume cur­rent dens­ity J=ρv and the Con­tinu­ity Equa­tion ∇⋅J=-dρ/dt
3 Mag­net­ic Field of a Straight Cur­rent Car­ry­ing Wire Via the Biot and Sav­art Law
4 Mag­net­ic Field of a Cir­cu­lar Cur­rent Loop Via the Biot and Sav­art Law
5 Deriv­a­tion of Ampere’s Law Two deriv­a­tions: An inform­al one and then a rig­or­ous math­em­at­ic­al one
6 Mag­net­ic Vec­tor Potential  
7 Bound­ary Con­di­tions on the Mag­net­ic Field Import­ant for elec­tro­dynam­ics: what hap­pens when the field is incid­ent on a surface/boundary
8 Vec­tor Poten­tial Mul­ti­pole Expansion Apply­ing an infin­ite power series expan­sion to the vec­tor potential
9 Mag­net­ic Torque on a Cur­rent Loop Required in order to dis­cuss motors and elec­tri­city generation
10 Bohr Mag­neton The dipole moment of a single orbit­ing electron
11 Mag­net­ic Polar­isa­tion : Magnetisation Para­mag­net­ism and diamagnetism
12 DC Motor and Generator Apply­ing the res­ult of video #9 and the mag­net­ic torque
13 Mag­net­isa­tion Bound Currents Mag­net­ic Polarisation

 

Mag­neto­stat­ics mag­neto­stat­ics maxwell’s equa­tions elec­tric poten­tial coulomb’s law Mag­neto­stat­ics mag­neto­stat­ics maxwell’s equa­tions elec­tric poten­tial coulomb’s law Mag­neto­stat­ics mag­neto­stat­ics maxwell’s equa­tions elec­tric poten­tial coulomb’s law Mag­neto­stat­ics mag­neto­stat­ics maxwell’s equa­tions elec­tric poten­tial coulomb’s law 

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