L29.2 Separation of variables - spherical polar coordinates - Example 3.6 P-II
#electrodynamics #griffiths #sayphysics
00:00 - Introduction: Writing the equation
00:02 - Substituting and expressing the equation as L' and L
00:14 - Deriving the equation for L
00:25 - Integrating with respect to the potential
00:38 - Solving the integral with Legendre polynomials
01:02 - Expression for the solution of Al
01:12 - Substituting Al into the equation
01:26 - Solving for Al when the potential is given
01:42 - Specifying the potential for the surface of the sphere
02:00 - Potential equation and calculation of Al
02:24 - Using a trick to simplify the equation
02:41 - Breaking the potential into components
03:05 - Rewriting the potential with Legendre polynomials
03:20 - Transforming the equation using the half-angle formula
03:37 - Simplifying the equation for sine and cosine terms
04:00 - Using identities to simplify the equation
04:26 - Recognizing the polynomials and their conversions
04:44 - Final simplified expression with Legendre polynomials
05:13 - Analyzing the next steps and solving the equation
05:59 - Comparing the potentials for simplification
06:21 - Identifying the terms involved in the expansion
06:44 - Expanding the equation for different L values
07:16 - Determining values for Al
07:42 - Finalizing the values of A0 and A1
08:25 - Concluding the solution with potential terms
08:57 - Final steps for determining A0 and A1
09:23 - Substituting the values of Al into the equation
09:52 - Simplifying the final potential expression
10:23 - Final solution for the potential
11:00 - Finalizing the result and solving the next problems
11:53 - Discussing upcoming examples (3.7, 3.8, 3.9)
12:04 - Encouragement for solving simplified problems
12:27 - Comparison with previous methods
12:36 - Transition to the next example involving potential outside the sphere
Example 3.6
The potential Vo(θ) is specified on the surface of a hollow sphere, of radius R. Find the
potential inside the sphere.
Snap of Board: https://drive.google.com/file/d/1ATQ4...
In this video tutorial, we solve Example 3.6 from the renowned textbook 'Introduction to Electrodynamics' by David J. Griffiths. We tackle the problem of finding the potential inside a hollow sphere when the potential Vo(θ) is specified on its surface. Using the method of separation of variables in spherical polar coordinates, we walk through the step-by-step solution to understand the intricacies of this electrodynamic problem. Whether you're a student studying electromagnetism or an enthusiast delving into advanced physics concepts, this tutorial offers valuable insights and clarity."
"Example 3.6 Griffiths"
"Electrodynamics tutorial"
"Separation of variables in spherical polar coordinates"
"Potential inside hollow sphere"
"Electrodynamics problem solving"
"Introduction to Electrodynamics"
"Physics tutorial"
"David J. Griffiths"
"Electromagnetism explained"
"Advanced physics concepts"
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