Physics 44 Magnetic Field Generated (13 of 28) Biot & Savart Law

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In this video I will explain and develops the equation of the Biot and Savart Law.

[GrandFatherMoon]

that one dislike if from the person who failed their physics test after watching this video

[dalenassar]

I have been searching years for something that I am yet to discover about a single charge moving in a straight line: You came close, but did not mention it. Here is the question:

I know (from all the videos on this), that the magnetic field varies as r^2 in the SAME PLANE as the moving charge, BUT, what is the GEOMETRICAL shape (not using the formula) of the magnetic field due to the SINGLE MOVING charge at points AHEAD of it??? My guess would be that they are concentric rings along the path (where the charge has NOT yet reached) and (probably exponentially) decay where the linear motion charge will be a bit later in time. Something like smaller and smaller conical rings ahead of the charge that decreases with distance from the charge location at present time.
PLEASE HELP!

[quanqingguo]

i am watching your video for years especially before the exam i went through all the confusing concepts. you have made it easy, simple and easy to understand. Thank you for all the amazing work :)

[ThilebanTheEngineer]

Thanks for this video. I think @1:22 you meant permeability constant.

[valeriereid]

Thank you Professor Van Biezen for making a very rigorous topic understandable. You are the best physics lecturer anywhere. I can always come to this channel for better understanding of where things come from in an equation.

[spurti]

But I have a doubt actually in my textbook the derivation is written like this dB=μ0[I (dL×r)]/4π•r^3
Using the magnitude formula for cross product we get dB=μ0 I dL•r sinθ/4π•r^3 & we cancel the magnitude of the r vector to r^3 and you get the final result that is
dB=μ0 I dL sinθ/4π•r^2 but in your video is shows that dB=μ0 I dL•r sinθ/4π•r^2. And I am baffled.

[oneinabillion]

Hi sir, you derived the same thing in video 4 but in another way... How is it different?

[Nick-jvow]

You are an amazing man, thank you so much for these videos

[astral_md]

Appreciated by your work ! Thank you sir !

[dalenassar]

Thanks for the great explanation--one thing...at about timestamp 3:28
you get to a point where the equations indicate that dQ is the amount
of charge in dl. You indicate also here that dl contains "q" the charge
of a single particle (ie electron?).
Here is where things start to get confusing to me: for the infinitesimal length dl, wouldn't even a single charge be way to big to fit into dl?
I'm thinking maybe just magnitudes of charge (not physical size) are what is important here??? So, is this assuming that what is inside dl actually is just dQ, where dQ represents only the magnitude of a the charge of a single physical PARTICLE rather than the actual particle volume? Thanks--I'm getting there. My goal is to learn the most I can about the
details of the creation of the fascinating Biot-Savart Law.

[aquadockemi]

How can the drift velocity be substituted for length and cross sectional area, with out it being per second?