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The scal­ar Elec­tric Poten­tial / Voltage is per­haps the most dif­fi­cult the­or­et­ic­al concept util­ised in the study of Elec­tro­stat­ics (the vec­tor poten­tial is util­ised in the study of Mag­net­ism). In this series of videos, I seek to dis­cuss and illus­trate all of the neces­sary the­ory in order for you to be com­fort­able with using it, its origins/derivation and why it’s neces­sary! A word of warn­ing though, all videos (with the excep­tion of #10 where I dis­cuss the phys­ic­al inter­pret­a­tion of the poten­tial / voltage) here require the stu­dent to have a grasp of Vec­tor Cal­cu­lus. I do make a par­tic­u­lar effort to per­form step by step deriv­a­tions — how­ever some­times that’s still insuf­fi­cient. I hope they can be of assistance!

Return to Elec­tro­mag­net­ism and Optics

Video # Video Tutori­al Title Remarks
1 The Helm­holtz Theorem A dis­cus­sion without a derivation
2 The Dir­ac Delta Func­tion 1/2 A motiv­a­tion of the function’s origins
3 The Dir­ac Delta Func­tion 2/2 Most import­ant video : A math­em­at­ic­al dis­cus­sion of its intrigue
4 Gradi­ent of one over the sep­ar­a­tion vector This func­tion is seen all over the study of Electrodynamics
5 Lapla­cian of one over the sep­ar­a­tion vector Required IOT derive the Helm­holtz Theorem
6 Helm­holtz The­or­em Deriv­a­tion 1/2 The scal­ar potential
7 Helm­holtz The­or­em Deriv­a­tion 2/2  The vec­tor poten­tial and the con­clu­sion of the derivation
8 Deriv­a­tion of the law of Biot and Savart Illus­trat­ing the beauty of the Dir­ac Delta Function
9 Elec­tric Potential Math­em­at­ic­al deriv­a­tion using the Helm­holtz Theorem
10 Elec­tric Potential Phys­ic­al inter­pret­a­tion of poten­tial (why we call it voltage)
11 Elec­tric Poten­tial Example 1/3 Spher­ic­al Con­duct­ing Shell
12 Elec­tric Poten­tial Example 2/3 Uni­formly Charged Sol­id Sphere
13 Elec­tric Poten­tial Example 3/3 Not yet recorded 🙁
14 Mul­ti­pole Expan­sion for the Elec­tric Potential Power series expan­sion of the scal­ar poten­tial ‘V’
15 Mag­net­ic Vec­tor Potential Using the Helm­holtz Theorem
16 Mul­ti­pole Expan­sion for the Mag­net­ic Potential Power series expan­sion of the vec­tor poten­tial ‘A’
17 Bound Cur­rents Mag­net­ic polarisation

 

elec­tro­stat­ics mag­neto­stat­ics maxwell’s equa­tions elec­tric poten­tial helm­holtz the­or­em biot and sav­art dir­ac delta func­tion elec­tro­stat­ics mag­neto­stat­ics maxwell’s equa­tions elec­tric poten­tial helm­holtz the­or­em biot and sav­art dir­ac delta func­tion elec­tro­stat­ics mag­neto­stat­ics maxwell’s equa­tions elec­tric poten­tial helm­holtz the­or­em biot and sav­art dir­ac delta function

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