L30.2 Separation of variables - spherical polar coordinates - Example 3.8
#electrodynamics #griffiths #sayphysics
0:00 - Introduction to Example 3.8: Understanding the Metal Sphere in an Electric Field
0:05 - Explanation of the Problem Statement in Example 3.8
0:14 - The Setup: Metal Sphere in a Uniform Electric Field
0:25 - Impact of Electric Field on the Metal Sphere
0:33 - Field Distortion Due to the Induced Charge
0:42 - Understanding the Charge Distribution on the Sphere
0:53 - Distorted Electric Field Lines Around the Sphere
1:03 - Visualizing the Distorted Field Lines
1:14 - How the Electric Field Lines Behave with the Sphere Present
1:35 - Analyzing the Distortion in the Electric Field
1:52 - The Distorted Field Lines Close to the Sphere
2:05 - Further Field Distortion Analysis
2:15 - Final Configuration of the Distorted Field Lines
2:30 - Understanding the Boundary Conditions for the Electric Field
2:50 - Far Field Behavior: Transition to Uniform Field
3:10 - Equations for Electric Field Lines Far from the Sphere
3:20 - Induced Charges and Charge Redistribution on the Sphere
3:43 - Boundary Condition and Potential Outside the Sphere
4:10 - The Influence of the Sphere on the Surrounding Electric Field
4:30 - Solving for the Potential Outside the Sphere
4:50 - Boundary Condition and its Implications for the Solution
5:30 - Deriving the Solution for the Potential Outside the Sphere
5:40 - Final Equation for the Potential in the Region Outside the Sphere
6:00 - Applying Boundary Conditions to Simplify the Solution
6:30 - Analyzing the Potential at a Distance from the Sphere
6:50 - Summarizing the Equation for Potential at Large Distances
7:10 - Deriving the Solution Using Special Functions
7:40 - Overview of the Boundary Conditions Used in the Calculation
8:00 - Introduction to the Summation Over Terms in the Solution
8:30 - Mathematical Solution Involving Spherical Harmonics
9:00 - Applying Boundary Conditions to Refine the Solution
9:30 - Final Form of the Potential Solution for r greater than R
10:00 - Conclusion and Final Remarks on Example 3.8
Example 3.8
An uncharged metal sphere of radius R is placed in an otherwise uniform electric field E = Eoz. [The field will push positive charge to the "northern'' surface of the sphere. leaving a negative charge on the "southern" surface (Fig. 3.24). This induced charge, in turn, distorts the field in the neighborhood of the sphere.] Find the potential in the region outside the sphere.
Snap of Board: https://drive.google.com/file/d/1tbWG...
In this video, we solve Example 3.8 from renowned physicist DJ Griffiths' Electrodynamics text. We tackle the intriguing scenario of an uncharged metal sphere placed within a uniform electric field. As we explore the implications of this setup, including the induced charge distribution and the resulting distortion of the electric field, we aim to elucidate the potential in the region exterior to the sphere. Join us as we employ separation of variables and spherical polar coordinates to unravel the intricacies of this fascinating electrodynamic problem.
"Electrodynamics example"
"Metal sphere in electric field"
"Uniform electric field"
"Induced charge distribution"
"Electric field distortion"
"Potential calculation"
"Separation of variables"
"Spherical polar coordinates"
"DJ Griffiths Electrodynamics"
"Electrodynamic problem solving"
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