Calculus 3: Divergence and Curl (31 of 50) Identity 7: CURL[CURL(F)]=Grad[DIV(f)] - (Grad)^2(F)

[@Priority9842]

This identity is a very important step in deriving the Helmholtz equation (wave equation) which describes the behavior of Electric field and Magnetic field propagation in isotropic, homogenous media.

[@Pklrs]

as well as solving Maxwell equations in vacuum

[@beverly6240]

YOU SAVE ME EVERY DAMN TIME. BLESS YOU MICHEL, THANK YOU FOR ALL YOUR HELP IN INTRODUCTORY NETWORK ANALYSIS AND NOW PROOFS FOR ELECTROMAGNETICS AHHH

[@piyushbishi6588]

But it became easy on taking a function.. What if it was any F?

[@sanskarrajput2846]

in the second example of laplace oprater you say ' if it applied on vector field then result is scaler quality and in this video when you applied laplace oprater a vector field then result is vector quality ,how?

[@MichelvanBiezen]

We are adding videos with more detail on the Laplace operator here: PHYSICS 67.1 ADVANCED E&M VECTORS kzbin.info/aero/PLX2gX-ftPVXWYLuDrKIF5npNwEDs4-vt6

[@Pawanduhan26]

@@MichelvanBiezen sir there are many videos...which one should I watch to clarify this doubt...you have used Laplace of vector to be scalar in one video and here you have taken Laplace of vector in vector form

[@jminl1912]

I wonder if when we set F as (x^2,y^2,xyz), it can involve the case where components of vector i or vector j should be under zero.

[@jellyfrancis]

Is this identity true in higher dimensions ? 🤔💓

[@sciencerz7460]

this is awfully similar to triple cross product of a vector? is that just a notation trick? cause an "operator" as a vector doesnt make sense to me... please help!!

[@MichelvanBiezen]

What specifically is troubling you about the video? (Note that this video just covers some of the identities of the curl and the divergence and probably holds little practical value).

[@sciencerz7460]

@@MichelvanBiezen sorry i didnt word it right(english is my second language) my professor was trying to prove that light is a plane wave using maxwells equations. he used this particular identity ,telling us that operators can be thought of as vectors and you can think of "a curl of a curl" as triple cross product of "delta delta and the field". (which doesnt make sense to me) my question was if this is just a notation trick or can you somhow really think of operators as a vector?

[@damarmurti]

I tried this identity on f = x^2y (x, y, z) but it didn't fit the identity. While the second derivative and gradient of divergence was acceptable, the result of the double curl to the vector messed it up. Is there any requisite or specific vector that couldn't be applied to this identity?

[@damarmurti]

Well, it seems that the variable which allowed to have more than one power (squared, cubed etc.) are the variable on corresponding axis. For example, on x-axis or i direction, the variable allowed to have more than one power is x. So does for the y-axis or j direction and z-axis or k direction.

[@anchalmishra5042]

Solve div(grad 1/r)=?

[@pvksmaheeth8816]

Sir how did you got 4:15 gradient of divergent(F) as (2+y)i+(2+x)j

[@d-nguyen5620]

take the derivative of div(F) respect to "x" and bring down to the i direction, the same as the j direction, take the derivative of div(F) which respect to "y"

[@gamersacademy8678]

tumse na ho payega ja re

[@vikasyadav9345]

Sir F=(x^2i +y^2j+xyz k^) I do not know how set the equation please tell me sir

[@gamersacademy8678]

bhai jab pta h foreigner wala h uska alag type me batayega toh kya kr rhha yaha🤣🤣

[@egb4638]

How come you dont just use the symbols and actually use real values?

[@MichelvanBiezen]

Not sure that I understand your question.

[@egb4638]

@@MichelvanBiezen im sorry, but I mean why do you not just use d/dx and so forth. Prove the formula just using the nabla signs and so forth.

[@MichelvanBiezen]

There are often multiple ways to solve a problem. What is shown is just one of the methods.

[@islam-kh3py]

Thanks sir. I'm from Bangladesh.🎉

[@MichelvanBiezen]

Welcome to the channel!

[@shubhamsahu5956]

Thanks a lot sir , hat's off to you.

[@MichelvanBiezen]

Glad you find the videos helpful. Thanks for your comment.

[@chandanprasad1503]

Thanx ❤

[@lathavedachalam89]

Sir why did you choose f vector is x^2 i+ y^2j+z^2k =f

[@MichelvanBiezen]

That is not the vector we choose, although it is somewhat arbitrary which one you choose.

[@nomadbigALI]

Come to METU

[@immanjeyaraj7245]

TQ sir for your details explanation

[@MichelvanBiezen]

You are welcome

[@swayamsarit5468]

Thank You ☺️

[@MichelvanBiezen]

You’re welcome 😊

[@alejandrohenriquez3688]

Thanks, gracias de Bolivia

[@MichelvanBiezen]

Hi and welcome to the channel!

[@rinabalapradhan5601]

Doesn't seeing this video what is doing

[@hashemsaaed4929]

we love you man

[@bibhisanabhuyan5659]

If 'f' is a solinoidal vector.Show that the curl curl curl curl f=(del^2)f.(del^2)f=(del^4)f Sir plzz explain this question answered

[@harshpastaria8120]

nice one.

[@munamohanned6404]

thanks

[@MichelvanBiezen]

Welcome

[@zahinrazeen5459]

The best

[@oldduckling2334]

TYSMMMMMM

[@MichelvanBiezen]

You are welcome. 🙂

[@Dragon-Slay3r]

Breaking news Bad piggies trying to fit the thick 7 inside the curl but it won't fit because the curl is curved from the top 🤣 I just thought I let you know what they're trying to do 👁️ 🤣

[@Dragon-Slay3r]

Breaking news they're trying to put a seahorse 7 with a square c horse inside the curl but its no good as it's too small 😂

[@Dragon-Slay3r]

Breaking news Now they trying to put the ace of clubs inside the curl aka 3 snooker balls as a tiny pyramid that might work but it might fall out as it's also small

[@Dragon-Slay3r]

Breaking news 7 back clip nah that won't work so they gonna try 7/8 squash in the curl 😂 ok no more just thought let them know I know their games

[@MichelvanBiezen]

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