Solving Poisson's equation ##\nabla^2\psi##

Thread starter AHSAN MUJTABA
Start date Oct 7, 2020

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SUMMARY

This discussion focuses on solving Poisson's equation, specifically in the context of a point charge above an infinite conducting plane. The method of images is highlighted as a crucial technique, allowing for the construction of solutions that satisfy boundary conditions, such as maintaining a potential of zero at the plane and at infinity. The uniqueness theorem is emphasized, confirming that solutions within a defined region are unique given fixed boundary conditions. Participants clarify that while the potential can be adjusted by a constant, the essential boundary conditions must still be satisfied.

PREREQUISITES

Understanding of Poisson's equation and its applications.
Familiarity with the method of images in electrostatics.
Knowledge of boundary conditions in potential theory.
Basic concepts of electric fields and surface charge density.

NEXT STEPS

Study the method of images in detail, focusing on its application in electrostatics.
Learn about uniqueness theorems related to partial differential equations.
Explore the derivation and implications of Poisson's equation in various geometries.
Investigate the relationship between electric fields and potential in electrostatic systems.

USEFUL FOR

Students and professionals in physics, particularly those specializing in electrostatics, mathematical physics, and electrical engineering, will benefit from this discussion.

Oct 12, 2020

AHSAN MUJTABA

PhDeezNutz said:

it matters for the problem as it was given to you. But it doesn’t matter in general because a potential is arbitrary up to a constant.

but it doesn't play part in charge density and other calculations as it is just a constant