An old nugget of a question: potential nucleus due to uniform charge sphere.

[niceguy]

Homework Statement

Ast stated above: Biut i just can't get the correct answer!

radius of sphere = a

charge ze contained

Homework Equations

by gauss: E= (ze)*r/4pi(epsilon)*a^3 at any point within the sphere.

and

dv=r^2*sin(theta)dTheta*dphi*dr

Energy density= 0.5*epsilon*E^2

The Attempt at a Solution

letting energy= integral(energy density)dv

with limits: r= 0-a, theta= 0-pi, phi=0- 2pi

i get wrong answer:

(ze)^2/80epsilon*pi*a ration between top and bottom, should be 3(ze)^2/20epsilon*pi*a any ideas?

many thanks!

 

[Jhero]

Thank you for sharing your question with us. It seems that you are trying to calculate the energy density within a charged sphere using Gauss's law and the energy density equation. However, there seems to be an error in your calculation. Here are a few suggestions that may help you get the correct answer:

1. When calculating the electric field using Gauss's law, the charge enclosed within the Gaussian surface should be the total charge of the sphere, not just ze. So the correct equation would be E= (Q/4pi*epsilon*a^2) at any point within the sphere.

2. When calculating the energy density, the correct equation is U= (1/2)*epsilon*E^2. It seems that you have used the electric field instead of the energy density in your calculation.

3. When setting up the limits for the integral, make sure to use the correct values for r, theta and phi. The limits for r should be from 0 to a, theta from 0 to pi and phi from 0 to 2pi.

I hope these suggestions help you get the correct answer. If you still face any difficulties, please feel free to share your calculations with us so we can further assist you. Good luck!