Maxwell’s Equations Part 1: Gauss’s Law for the Electric Field

It's time to go a little deeper with our understanding of classical physics! From the very introductory conceptual tutorials on electricity and magnetism, we need to apply some more rigor and use advanced math that will help us really understand these topics. To start we will examine Maxwell's equations. These are the gold standard for describing electromagnetic fields. If the math looks unfamiliar be sure to visit my mathematics playlist for some review. First up, Gauss's law for the electric field!
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[@ychentt]

This is an absolutely beautiful content. It’s unbelievable that we have the privilege to watch this for free. Thank you professor Dave.

[@glennpearson9348]

Magnetic field strengths and triple-loop integrals! My favorites from Physics 201! Thanks for the refresher, Professor Dave!

[@supercompooper]

My second year physics exam: "from first principles derive Maxwell's equations in both integral and differential forms". 6 hours. GO! 😮😊

[@PensiveMoose]

Couldn’t come at a better time. I’m taking my qualifying exams soon and I need this review. Thank you so much!!

[@leuchapolo]

Just want to say you're an absolute legend and doing a wonderful thing for this world. Keep up the good work and thank you.

[@valleyofsin]

Really enjoy the tutorials. Takes the unnecessary lingo out and builds it up from the bones so it's easier to grasp.

[@nicco-sixty]

Can you make some videos on differential equations?

[@armandoski-g]

Oh man! It was about time to drop these Maxwell's Equations videos!! Really excited to see the rest :)

[@BrentLeVasseur]

Nice simple explanation! However, the topology of a monopole charge is a sphere, while the topology of a dipole charge is actually a torus shape. And also there are two fields simultaneously at play, the electric field and the dielectric field. The electric field is a transverse wave oscillation that manifests from the dielectric field impulse at each oscillation. The dielectric field in a dipole charge is a scalar and longitudinal impulse, and is shaped like two inverse cones that meet at the point of charge, while the electric field is a torus shape that surrounds that charge with the holes in the torus formed by the two inward facing cones of the dielectric field.

[@peterheath7960]

I love Mathematics. Pure, pure, pure.

[@polarisukyc1204]

Your content is brilliant, honestly the best educational content on KZbin, I have a bit of an ask, will you do some videos on plasma physics, I cannot find much info on it

[@ayokunleobayomi8314]

Thank you Professor dave

[@aztheking6280]

i can't wait for the next parts superb quality as usual , keep it up

[@KoRntech]

I look forward in using some of this when I'm teaching Extra Class licensing for Amateur Radio. Some want to really know the physics and I'm not a good source as I'm rusty myself, and most communicators about RF design and and electrical fields on YT are way way older.

[@oribadyl8036]

Funfact: divergence theorem is called "Gauss and Ostrogradsky theorem" in Polish literature. Funny coincidence, for it to be used to evaluate Gauss law in integral form from it's differential form

[@revan2549]

Chemistry Jesus knows everything. You helped me a lot. Thanks, Math/Chemistry/Physics/Biology Jesus!

[@oldtimegames96]

I'm laughing my head off cuz you called him Chemistry Jesus ( as in, how come I didn't see that Prof. Dave looks like a short haired version of Jesus)

[@Claudius_Ptolemy]

Will there be an episode explaining Candela, Lux and Lumen ?

[@Lennon959]

Hi sir. Can you make a vid about Plasmons after Maxwell Equations? I don't fully understand this. Like how to prove that the EM wave will be reflected when the frequency of EM wave is less than the Plasma frequency of materials, by using Maxwell equation? How the metals have Electric Fields in plasma oscillations if metal's permittivity is infinite? thank you in advance.

[@mcalkis5771]

Bruh where was this four months ago when I had my exam?? Thanks Dave!

[@0cgw]

The normal to a sphere is not constant (it is radially outwards) and varies at every point on the sphere. It is also a vector, so the explanation at 8:30 is incorrect, What you need to say is that vector E=E(r)n where E(r) is the magnitude of the electric field at radius r. Then E.n=E(r), which is independent of position on the sphere. Only then can you take it outside the integral.

[@wernerlippert5499]

makes sense to me

[@Nxck2440]

@@Jay-kw2kb Prof Dave was simplifying, and he never demonstrated any example where the vector form was actually needed so it's not that big of a deal

[@spacecowboy5274]

How E.n = E(r)??

[@0cgw]

@@spacecowboy5274 E and n are vectors, with n radially outwards. E(r) is the component of E radially, so E=E(r)n, and hence E.n=E(r).

[@spacecowboy5274]

@@0cgw E=E(r)n how did u get this?

[@got-iit5391]

Question - if you have a square 1-ton block, and you have four magnets attached to the bottom side of this block. This block is centered on another block, balanced. If you had a platform on the ground underneath this balanced block and it had four opposing magnets positioned in a larger circumference from the block, could you lift the platform up, and by doing so, would lift up the 1-ton block. Would this weight be the same as if you just tried to lift the block up without magnets or would the opposing magnetic force lift the 1-ton block for you much easier? P.S. - I know very little about magnetism...

[@mrstevenmeloney]

I love Professor Dave

[@andrewlees9056]

Does Gauss' law only apply for static charge or will it also apply for charges in motion?

[@totogashloog2162]

I needed this, thanks daddy dave

[@tobiasmohwald1530]

Pls more of Electric enfeneering

[@sciencenerd7639]

awesome, physics!

[@garrettchambers9005]

Do more EnM, this is one of my EnM semesters and its killing me, separation of variables?

[@A.Hisham86]

Well, the scenario 1, shouldn't be the electrical field zero? There's no charge in the sphere, only at the surface.

[@demarcuscousinsthe65th]

Hello dave

[@WippSheridan]

Hmm, I think the Displacement vector is not the dot product of permittivity and the electric field. It's just the product however, not the dot product.

[@backstreetfan2887]

thanks

[@sai1962]

Can you make a video about mathematical induction?

[@AnishK-go2ef]

nice

[@btchhangte4481]

Please explain Protein kinase R

[@phraydedjez]

Dave's not here man

[@mearionet]

more physics lets gooo

[@FamilyTreeRG]

Hey Dave! What are your thoughts on tom Campbell’s MBT science model?

[@CLIOBEAR]

2:44

[@victorfrank2629]

U remind me of my High School

[@velialomeli4441]

According to my calculations that's true

[@ayokunleobayomi8314]

Hi professor Dave, Can you make a video on Host tolerance to pathobionts? I need more insight on it I really enjoyed your previous video on pathobionts. I've tried contacting you via email and linkdin already 🙂

[@ayokunleobayomi8314]

Please take a look at your email sir

[@Bretaxy]

@@ayokunleobayomi8314 Calm down

[@ThereIsNoMatch]

I love you

[@jackhamerordewey9552]

Perfect explanation!!

[@souleymanegassama7566]

why this videos are not in frensh 😭😭

[@winchesterbear]

You don’t deduce Maxwell’ equations. You induce them. Deducing them would require QED.

[@ProfessorDaveExplains]

I didn’t say deduce I said derive.

[@Cheesesteakfreak]

Hi Prof Dave. I have a request, if you could revisit the anti-vax denial issue - there's still so many anti-covid vaxxers out there. Just a request, thanks for your work.

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🤭😜

[@johannes68]

I agree

[@alessandrorossi1294]

He’s not a REAL professor…

[@besotoxicomusic]

What was wrong with his first one that he needs to revisit it?

[@Wing578]

@@alessandrorossi1294 He was though he taught in a university.

[@-JA-]

🙂👍

[@DarthEstring]

The Jesus of Science

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I believe the earth is flat

[@sanjivinsmoke1642]

Second to comment

[@smc64130]

I have three grandsons. I'm going to tell them everything they need to know they can learn from Professor Dave.

[@flaps805]

More like Maxwells fart

[@family-accountemail9111]

great!