2.3.3 Poisson's Equation and Laplace's Equation

Taking the divergence of the gradient of the potential gives us two interesting equations.

[jg]

Yes, I'm missing a negative sign.

Potential is a neat way to describe conservative forces. The derivative of the potential is the force you would experience at that point. A net force is the acceleration of the object (with factor m mass). So the gradient of the potential will give you the acceleration at a point.

This is from introductory physics. Hopefully potentials and forces and acceleration is not too foreign a concept.

[AmeerHamza-tvjv]

I am from Pakistan. Your explanation method is very easy, you explane a topic in a very short time in a logical manner. I like it😋

[林佑倫-cz]

Thanks a lot! I am a student in Taiwan. These videos do help me a lot.

[jg]

gradient is just "nabla f". Divergence is "nabla dot f". The dot makes all the difference.

Also, gradient works on a scalar function, while divergence works on a vector function.

[yupiiyummy]

Hello, I think you missed a negative sign for the Poisson's equation (not sure if it's that is really important), however, if taking the negative sign into account, what you said at 1:07 ("Potential basically accelerates...") is it always true?
Thanks! Love your videos btw :)

[UnforsakenXII]

Thanks for supplementing my reading. : D

[kfp]

The last bit is only true for a region in which ∂B/∂t = 0, where B is the magnetic field, right? Otherwise, the changing magnetic field causes a potential difference, as given by ∇ x E = -∂B/∂t...

[jordandanielangulo]

thankyou very much for this video, however, can you make a way that your comments on vids can make it through offline? i have downloaded your vids ( using the youtube app ) and i struggle because of some missing negative signs etc. thanks

[divitagautam]

How can we solve the problems of non uniform charge density using Poisson's equation?

[k.rachana]

Derivation part for each coordinated system don't explaned sir..but it's okay to understand

[johnnyboi]

Do the gradient and divergence operations have the same symbols?

[DilrajSharma]

We call it cross instead of curl in India
And curl means partial differentiation here

[twopieye]

Second spatial derivative is curvature, not acceleration.