L27.3 Separation of variables - Cartesian coordinates - Example 3.5 P-I
#electrodynamics #griffiths #sayphysics
00:03 - Introduction to Example 3.5
00:07 - Overview of the 3D problem
00:12 - Explanation of the setup for the rectangular metal pipe
00:21 - Description of the grounded side and potential at x = 0
00:33 - The potential setup inside the pipe
00:39 - Discussion of the boundary conditions for the problem
00:47 - Boundary condition at y = 0 and y = a
02:08 - Boundary condition at z = 0 and z = b
03:01 - Boundary condition at x = ∞ and x = 0
04:21 - Introduction to the separation of variables technique
04:31 - Writing the potential as a product of functions of x, y, z
04:59 - Substitution into the equation and separation of variables
05:09 - Deriving the equations for each variable: x, y, z
06:00 - Deriving the equation for the x component of the potential
06:52 - Introducing constants for separation of variables
07:19 - Solving for the constants and assumptions
08:00 - Applying mathematical tricks to find the solutions for k² and l²
08:56 - Final results for the equation for x
09:20 - Solving for the equations for y and z
09:49 - Final equation for z
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.
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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