Dot Physics
Derivation of the Capstan Equation - Frictional Force due to a String Wrapped Around a Circle
updated
Here' s the python code
trinket.io/glowscript/37afcc3dc339
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Here's an example with a charge and a non-spherical dielectric.
Python code here
trinket.io/glowscript/31268eca4acf
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
What is the displacement field? What is the electric field? What is the change in potential?
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
youtu.be/I6yWKB9CO3A
Now, let's see if we can model this same field using 2000 internal dipoles. Here's the python code.
trinket.io/glowscript/49efb6a9d69a
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Problem 4.15
A thick spherical shell (inner radius a, outer radius b) is made of a dielectric material with a "frozen-in" polarization.
P = k*rhat/r
where k is a constant and r is the distance from the center. Find the electric field in all three regions by two different methods.
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
1. What is polarization and the dipole moment
2. Free charges vs. bound charges
3. Gauss's Law
4. Derivation of displacement field
5. Why?
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Here is my very basic derivation along with a python calculation for the surface charge density on an insulating sphere.
Code here:
trinket.io/glowscript/8f720cc084ca
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Here we look at the polarization of an atom due to a charge and then calculate the force between the charge and neutral atom.
After that, I model the interaction between a point charge and an insulating cube using python. Here is the code
trinket.io/glowscript/67875fbcb878
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
python code here
trinket.io/glowscript/7110267c9173
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Here is my python code
trinket.io/glowscript/e8862fe28b18
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Jupyter notebooks - anaconda.com
VPython - vpython.org
You will need to install two things:
all the python stuff: anaconda.com
VPython: vpython.org
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
How do you derive the electric potential and field due to a dipole? Bonus visualization with python
Here is the python code
trinket.io/glowscript/5feabdff5b39
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Here is the python code
colab.research.google.com/drive/1p9AZV6cNmEzKR8Dvva_efE6JxDGsnSlG?usp=sharing
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
In a previous video (here youtu.be/M3RDynwsFuw ) I used separation of variables to find the electric potential in a 2D space.
In this video, I'm going to repeat the calculation using finite values of the potential and the relaxation method in python.
Here is the python code
trinket.io/glowscript/0e378f033144
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Two infinite grounded metal plates lie parallel to the xz plane, one at y = 0, the other at y = a. The left end, at x = 0, is closed off with an infinite strip insulated from the two plates and maintained at a specific potential Vo(y). Find the potential inside this “slot.”
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
In a previous video, we looked at the method of images to find the potential due to a charge and a grounded conductor. In this video, we model the motion of charges in the plate with a many body problem.
Here is the previous video:
youtu.be/ePjfCd1UaQ8
Here is the python code.
trinket.io/glowscript/21360ba6515d
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Find the electric potential due to a charge above a flat conductor. What is the charge density on the plate and what is the total charge?
Yes, my final answer is off by a factor of 2 - I'm sure it was just a silly mistake.
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
youtu.be/1va2J248nuE?si=HS6Cx8LnodFE6OAp
Using conservation of momentum, and video analysis, we can get an estimate for the mass of the orb. Here, I'm using Tracker Video Analysis
opensourcephysics.github.io/tracker-website
Here is the python code for the visualization (with the data)
trinket.io/glowscript/a02e16bc366b
Finally, here is a video showing how to model collisions in python
youtu.be/miqlwBXxWJE
The Laplace equation in 1D is fairly straightforward (it's literally a line). However, this is a good opportunity to practice solving it numerically.
Here is the python code
trinket.io/glowscript/158f44d77526
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
In this video:
- Electric field due to a plate
- Electric field due to parallel plates
- Electric potential between two plates
- Capacitance
- Energy density of electric field
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Problem 2.21
Find the potential inside and outside a uniformly charged solid sphere whose radius is R and whose total charge is q. Use infinity as your reference point.
Bonus: Numerical calculation with python: Here is the code.
trinket.io/glowscript/b999fe3746bb
Double bonus: finding the electric potential for a shell of charge
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Here is the python code
trinket.io/glowscript/021d6b35f6b4
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Problem 2.10
Find the electric flux through one side of a cube.
In this case, I create a 3D model of the area and the field to visualize the flux. Here is the python code.
trinket.io/glowscript/980df792833c
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Problem 2.10
A charge q sits at the back corner of a cube. What is the flux of E through the shaded side?
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Problem 2.9
Suppose the electric field in some region is found to be E = kr^3 in the spherical coordinates. a) find the charge density rho. b) find the total charge in a sphere of radius R
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Problem 2.7
Find the electric field a distance z from the center of a spherical surface of radius R that carries a uniform charge density sigma. Tread the case z less than R (inside) as well as z greater than R (outside).
In this case I use a numerical model to calculate the field.
Here is the code.
trinket.io/glowscript/57772a76ebff
Here is the previous video (setting up the solution with an integral)
youtu.be/g_h_hQwMOAI
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Problem 2.7
Find the electric field a distance z from the center of a spherical surface of radius R that carries a uniform charge density sigma. Tread the case z less than R (inside) as well as z greater than R (outside).
In this case I use a numerical integration to solve evaluate the final integral. Here is the code.
trinket.io/glowscript/63b4ba968d81
Here is the second video with a numerical model for a finite number of charges
youtu.be/kyxtkrNrWoQ
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Here is the code
trinket.io/glowscript/3699aa399011
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
In this video:
- Electric field due to a point charge.
- Electric field due to charge distribution
- Gauss's Law
- Differential form of Gauss's Law
- Electric potential
- Capacitors
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Problem 2.5
Find the electric field a distance z above the center of a circular loop of radius r that carries a uniform line charge lambda.
Here is the python code
trinket.io/glowscript/c46944f71d06
Problem 2.5
Find the electric field a distance z above the center of a circular loop of radius r that carries a uniform line charge lambda.
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Example 2.2
Find the electric field a distance z above the midpoint of a straight line segment of length 2L that carries a uniform line charge lambda.
But this time, I calculate the electric field using python and a numerical integration
Here is the python code
trinket.io/glowscript/e484648fc534
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
Example 2.2
Find the electric field a distance z above the midpoint of a straight line segment of length 2L that carries a uniform line charge lambda.
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL
How do you make a spherical distribution of charges? Here are three different methods.
Python code:
Cartesian grid trinket.io/glowscript/5ac6230d4009
Spherical dist trinket.io/glowscript/b2154851cef1
Random dist trinket.io/glowscript/976ce0490305
Here is the playlist for the full course
youtube.com/playlist?list=PLWFlMBumSLSYDQww1iwZXEyNJb6xnoxZL


