L28.1 Separation of variables - Cartesian coordinates - Example 3.5 P-III
#electrodynamics #griffiths #sayphysics
00:00 - Introduction to Equation Setup
00:10 - Understanding the Double Summation
00:24 - Correcting the Variables for Z-Component
00:37 - Potential and Trigonometric Functions
01:09 - Equation Formulation and Corrections
01:12 - Importance of the Corrected Notation
02:15 - Evaluating at x=0 v0
03:15 - Revisiting Integral for Coefficient Calculations
03:33 - Derivation of Constants Using Kronecker Delta
04:16 - Solving for Cnm
05:00 - Integral Setup and Evaluation Cnm
06:00 - Integral Integration for Sine Functions Cnm
07:10 - Evaluating the Resulting Integral for Constants
08:30 - Calculating and Verifying Coefficients
10:14 - Final Expression for Cnm
12:11 - Integration and Finalization of Constants
14:09 - Substituting Cnm
15:05 - Conclusion of Solution
Example 3.5
An infinitely long rectangular metal pipe (sides a and b) is grounded, but one end, at x = 0, is maintained at a specified potential Vo (y, z), as indicated in Fig. 3.22. Find the potential inside the pipe.
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In this video, we delve into the solution of Example 3.5 from "Introduction to Electrodynamics" by David J. Griffiths. We explore the fascinating scenario of an infinitely long rectangular metal pipe with sides of dimensions a and b, where one end at x = 0 is maintained at a specified potential Vo(y, z), as illustrated in Fig. 3.22. Join us as we uncover the methodology to determine the potential inside the pipe, unraveling the intricate concepts of electrostatics.
"Introduction to Electrodynamics"
"David J. Griffiths"
"Example 3.5 solution"
"Infinitely long rectangular metal pipe"
"Electrostatic potential"
"Grounded metal pipe"
"Specified potential Vo"
"Electrostatics"
"Rectangular pipe dimensions"
"Electromagnetic theory"
"Electrostatics example"
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