- #1
Elvis 123456789
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Homework Statement
What is the gravitational potential both inside and outside a spherical shell of inner radius b and outer radius a?
Homework Equations
φ = ∫g⋅da = -4πGMencl
g = d∅/dr in the r hat direction
The Attempt at a Solution
I can get as far as getting the gravitational field for the three parts of the shell but I am not really sure how to determine the limits of integration in order to get the potentials
for (R > a) g*4πR2= -4πG*(4/3*π(a3-b3)*ρ)
then ∅ = ∫[G*(4/3*π(a3-b3)*ρ)]/R2 dr
for (b< R < a) g*4πR2= -4πG*(4/3*π(R3-b3)*ρ)
g = 4/3*πρG*(b3/R2 - R)
∅ = ∫-[4/3*πρG*(b3/R2 - R)] dr
for (R < b) g = 0 because there is no enclosed mass
and ∅ = constant the constant being determined from the integration limits
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