Bound charge density: why does ρ = -∇⋅P?

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Dr Ben Yelverton

Dr Ben Yelverton

Күн бұрын

Пікірлер: 20
@omarazami7377
@omarazami7377 Ай бұрын
Terrific video!! Griffiths only allow us to visualize uniform polarization (and therefore only surface bound charges). It makes perfect sense that if the polarization is changing (I.e. has a derivative) then charges “don’t cancel out” internally. I’m going to show this to a student I’m tutoring. Thank you again!!
@DrBenYelverton
@DrBenYelverton Ай бұрын
Excellent, I'm glad it was helpful!
@amittksingh
@amittksingh 11 ай бұрын
Thankyou for the last part where you explained on physical grounds why there will be a negative charge.
@DrBenYelverton
@DrBenYelverton 11 ай бұрын
No problem, always interesting to try to understand equations intuitively!
@TheJara123
@TheJara123 Жыл бұрын
Interesting presentation, man, thank you
@DrBenYelverton
@DrBenYelverton Жыл бұрын
Thanks, glad to hear it! Will be posting some more videos on dielectrics soon.
@MathwithMing
@MathwithMing Жыл бұрын
3:05 "By conservation of charge..." I have a question: why does the conservation of charge implies that the charge q_y(x,y,z) on the right face of the cube is balanced out completely by the charge on the left face, rather than by the charge on the other five faces (left, front, back, upper, lower) combined? Perhaps I'm missing something
@DrBenYelverton
@DrBenYelverton Жыл бұрын
Good point, the conservation of charge alone is not enough to imply that. However, we know that the effect of each component of the applied field is to pull positive charges in one direction and negative charges in the exact opposite direction, from which the result follows.
@MathwithMing
@MathwithMing Жыл бұрын
That makes sense, thanks!@@DrBenYelvertonDoes this argument still stand if the material is anisotropic tho?
@DrBenYelverton
@DrBenYelverton Жыл бұрын
@@MathwithMing Yes, because there will still be a dipole induced in some direction, which can always be thought of as the sum of three orthogonal dipoles perpendicular to the faces of the cube. The only difference would be that P is no longer parallel to E, but that doesn't affect the logic as our derivation depends only on P, not E.
@MathwithMing
@MathwithMing Жыл бұрын
@@DrBenYelverton Right! I’m still used to always think in terms of E and that’s how I got confused! Great explanation, thank you!
@MathwithMing
@MathwithMing Жыл бұрын
Very intuitive! Can we derive it using Gauss’s divergence theorem for an arbitrary surface?
@DrBenYelverton
@DrBenYelverton Жыл бұрын
We can indeed - see e.g. the Feynman Lectures, Vol 2, Chapter 10, for details! The method I used here is ultimately equivalent though, since proving the divergence theorem usually involves splitting the volume into small cube-shaped elements.
@MathwithMing
@MathwithMing Жыл бұрын
@@DrBenYelverton wow thanks for the reference! Will check it out!
@DrBenYelverton
@DrBenYelverton Жыл бұрын
The Feynman Lectures are absolutely my favourite Physics resource - very helpful for understanding things intuitively! I haven't read them all yet but am gradually working my way through them. All freely available via the official website too.
@mxminecraft9410
@mxminecraft9410 Жыл бұрын
Sir can you please make a video on all the mathematics or mathematical tools we require to study physics at different levels .
@DrBenYelverton
@DrBenYelverton Жыл бұрын
That's a big topic, I'd need to spend some time thinking about how best to approach that!
@mxminecraft9410
@mxminecraft9410 Жыл бұрын
@@DrBenYelverton ok sir
@douglasstrother6584
@douglasstrother6584 7 ай бұрын
Calculus, Linear Algebra and Differential Equations will take you far.
@Hussam-t4m
@Hussam-t4m 24 күн бұрын
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