Does the Triple Integral Formula Apply to a Point-Mass Inside a Spherical Shell?

AI Thread Summary
The discussion centers on the application of the triple integral formula to calculate the gravitational potential of a point mass inside a spherical shell. The formula -Gmρ2π(R_2^2-R_1^2) is questioned for its validity in this context. The potential outside a homogeneous sphere has been established, and the challenge is to derive the potential inside the shell using previous results. There is uncertainty about whether it's appropriate to combine the potential formulas for different radii. The conclusion is that the provided expression for potential appears incomplete or incorrect for the scenario described.
cscott
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Does -Gm\rho2\pi\left(R_2^2-R_1^2\right) make sense for the potential of a point-mass "m" inside a spherical shell of radii R_1< R_2 and density \rho?

Now I've already found the potential outside of a homogeneous sphere of same density. I'm now asked to use these two results to find the potential inside a homogeneous sphere of again indeity density sphere, using the previous two results.

Can I do this by considering the point on the inside of the shell with a sphere in the space in the middle? Does it make sense to add the two potential formulas using the correct radii?
 
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Expression for potential is GMm/R. So something is missing in the given expression
 
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