AP Physics C - Electric Potential of Charge Distributions
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- เผยแพร่เมื่อ 14 ม.ค. 2013
- A brief introduction to finding the electric potential of continuous charge distributions for students in calculus-based physics courses such as AP Physics C: Electricity and Magnetism. For more information, please visit APlusPhysics.com.
Thanks again, Dan! Electric potential is one of the more abstract ideas that I've come across so far in my study of physics and your videos are helping me to understand it better.
Great to hear from you Cody! I agree, electric potential is a very difficult concept -- good news that it's starting to come together for you.
Glad these are helping -- best of luck on your exam!
you are saving my life!! i dont feel so hopeless for my exam now. thanks a bunch!! :)
Awesome! been looking everywhere for this!
Glad you like it!
For the EP due to Charged Disk, should the little r become R in the final answer? Sqrt of [(z^2+R^2)^1/2 -z]
Thanks for the great video!
@potential due to a spherical shell, is r longer than R? Does r denote a distance to some point outside of the shell?
For the problem with the charged disk asking for electric potential:
Wouldn't you have to use V cos(theta) since the vectors parallel to the disk would cancel out?
thank you sir... im from india and this is in our syllabus also... its of great help!🙏🏻
how can calculate the electric potential when you have volume charge
thanks Dan ,this is the real deal.
Hi Dan, thanks a lot for ur classes!! that’s really helpful. But I have a simple question. In 13:01 in the video, you wrote that V inside need to integrate from infinity to capital R, but why should we take infinity into account if what we are calculating is the eclectic potential inside the shell. Shouldn’t we just do the integral inside the shell instead?
You're very welcome!
The last example doesn't make a lot of sense. I don't understand how you keep switching from R^3 to r^2 when calculating the potential when we are supposed to be using the electric field for the two integrals.
Shouldn't the last two integrals be identical but with different bounds?
thank you
Quick question. When calculating the electric field for these same configurations, you need to take into account that there is an angle theta, and you need to put in a cosine of theta to make sure the integral only sums up the components that point along the axis. Why do you not need to do this here? I understand that voltage is a scalar, but still, how does the math know that part of each little dV is cancelling out another little part of dV from somewhere else on the ring?
Hi vinnv226... because potential is a scalar, we actually don't have little dV's canceling each other out, all we have to do is add up all the little pieces. The directions don't matter at all.
Ah ok that makes sense, thanks so much for the video, it's really helpful as your videos always are ^_^
vinnv226 You're very welcome, and good luck!
should it not be sqrt(z^2 + R^2) - z, where you have a small r instead of capital R?
For the final answer yes, you are correct.
Thank u very much! But I have a problem like why u somtimes integrate dq to Q and othertimes u replace dq as sigma lamda or row then integrate and here in some cases u didnt use V=-{E.dl or is it a 2 method process? Plz help
ali hmede Hi Ali. These are all different strategies to solve the various problems. There is no one right way, I try to demonstrate a variety of techniques.
Dan Fullerton thank u very much sir!
@1:58, why is r sub i just R? Is the distance from the point P to any point on the ring the same for all points?
JackySub yes
thank you. after 7 years...
So when we say kQ/r is r in respect to the center of the shell... or what does that distance represent?
r is the distance from the charge to the point of interest (i.e. point P where you want to know the electric potential).
Thanks for this video, but in 13:58, why is the first part of the graph a constant?
Note how just above the graph we calculated the potential inside the shell, and found it was a constant (Q/(4*Pi*e_0*R), where R is a constant. Be careful here, R is a constant, the radius of the shell, little r is our variable.
Thanks!
Welcome!
What's the difference between dQ and ∆Q? Why did you set up the little charge as ∆Q on the first example and dQ on the second example?
Delta-Q is some small amount of contained charge. Our calculus principle is we're going to make that region smaller and smaller and smaller until it is infinitesimally small, which is represented by the differential Q (dQ).
@@DanFullerton Alright, but why did you you delta Q for the first example and dQ for the second example? Weren't you intending to set up a small amount of charge in both examples?
For the surface area of the sphere, why did you use little r instead of big R? I thought the surface area can be treated as a constant?
The radius of the actual sphere is R, the radius of my Gaussian surface, also a sphere, is little r (the variable that we integrate over).
Dan Fullerton Oh I see, thanks!
Another great vid.
For problem @ 15:00...
Isn't Qenc = Q? This would make E = Q/(4*pi*e0*r^2) which is essentially what you have if you take R to be = r and divide r / R^3. It would eliminate the extra steps (using 'rho').
Also according to your equation 'rho' = Q/V and Qenc = 'rho' * V
This means Qenc = (Q / V) * V = Q anyway.
Trying to understand why you wrote it like you did.
Hi ibzdude. You are right in what you are stating, though what I'm trying to demonstrate in the problem is an algorithm / process for solving Gauss's Law problems. In this case you could skip some of the steps, but as problems become more complex, following the same demonstrated methodology will provide a straightforward repeatable method of obtaining a solution.
For the potential inside the shell problem, why did you have to include the potential outside the shell from infinity to the radius of the shell? I thought the potential would just be zero, since we were just finding potential in the shell?
We're setting our arbitrary reference of 0 at an infinite distance away from all charges (really the only true reference that makes sense in a problem like this).
Thanks, also for the last problem, how did you know when to use lowercase r and uppercase R? How come lowercase was used for the area and the volume of the sphere but uppercase was used for the density?
What are the chances that you'll make videos for a university Physics course that explored Waves/Optics/Modern(Nuclear) Physics?
I have algebra-based videos on those topics, but unfortunately calculus-based videos on those topics are a ways away (my to-do list has me booked up with at least one year's worth of projects currently). If you think there would be a reasonable audience, though, I'll consider adding it to the list!
Dan Fullerton for sure! your videos are helping me get through my Physics 101 and 102 (Mechanics/Thermo/E&M) classes at college and I'd love to see more.
nice last name! I was born in Fullerton LOL
anyways thanks for the video!
My pleasure!
not sure if you are still alive but for the spherical shell of charge Q, wouldnt Voutside just be R to inf and Vinside 0 to R?
Still alive, and no (as per video).
@@DanFullerton Wow, didn't expect a response. Yeah took me a while to get my head around it. Thanks though!
for the disk
r-sub-i, dr, r, and R.....
god help me
If it were easy, they'd call it chemistry. ;-) (kidding!!!)
Why dont you just say K?
Great question -- as we progress in Physics C, the 1/(4*Pi*Epsilon_0) expanded version of k will allow you to simplify expressions in ways you might not see with just k written there.