Electric Potential by Integrating Poisson's Equation

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The discussion focuses on solving for the electric potential \varphi(r) of a spherical charge distribution using Poisson's equation. The initial attempts involved integrating the Laplacian in spherical coordinates, but the results were incorrect due to misapplication of integration rules. Participants emphasized the importance of recognizing spherical symmetry, leading to a simplification of the Laplacian and the need to solve a second-order differential equation. The conversation also highlighted the continuity and finiteness of the potential and its gradient, particularly at the origin and at the boundary of the charge distribution. Ultimately, the correct approach involves ensuring the potential is continuous and finite everywhere, particularly at the surface of the sphere.
  • #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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