Electric Potential by Integrating Poisson's Equation

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Homework Help Overview

The problem involves finding the electric potential \(\varphi(r)\) for a spherical distribution of charge with a constant charge density \(\rho\) within a radius \(R\) and zero charge density outside this radius. The approach suggested is to integrate Poisson's equation, which relates the Laplacian of the potential to the charge density.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various integration techniques for solving Poisson's equation, including the use of spherical coordinates and the Laplacian in spherical symmetry. There are attempts to evaluate integrals and derive expressions for the potential, with some participants questioning the correctness of their results and the assumptions made.

Discussion Status

The discussion is ongoing, with participants providing feedback on each other's approaches and clarifying the mathematical steps involved. Some guidance has been offered regarding the integration of the Laplacian and the implications of spherical symmetry on the potential function.

Contextual Notes

Participants are navigating through the complexities of integrating differential equations and are encouraged to consider the implications of boundary conditions, particularly the behavior of the potential inside and outside the charged sphere. There is an acknowledgment of the need to define constants appropriately in the context of the problem.

  • #31
Hi
I need some help with understanding like i have this poisson's equation from which i have to determine the potential by integrating ofcourse using the boundary condition phi=0 at x=plus or minus L/2 and that differentiation of phi with x is zero at x=0.

I see that they have arrived at the equation
phi= 1/2 rho/epsilon* (square of L/2 - square of x)

I don't know how they got this.

Note: How can I type physics symbols here?

Thanks
 
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  • #32
appsci said:
Hi
I need some help with understanding like i have this poisson's equation from which i have to determine the potential by integrating ofcourse using the boundary condition phi=0 at x=plus or minus L/2 and that differentiation of phi with x is zero at x=0.

I see that they have arrived at the equation
phi= 1/2 rho/epsilon* (square of L/2 - square of x)

I don't know how they got this.

Note: How can I type physics symbols here?

Thanks

Please create a new thread for your problem, and follow the homework template. Make sure you post the entire problem just like it is asked in your assignment.
 
  • #33
gabbagabbahey said:
Please create a new thread for your problem, and follow the homework template. Make sure you post the entire problem just like it is asked in your assignment.

Thanks. I will do so but can I know how to type equations or insert symbols over there.

Regards
 
  • #34
There is an introduction to using \LaTeX in these forums in this thread
 

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