- #1
Ananthan9470
- 32
- 0
I am asked to find the total gravitational energy of a hollow sphere using the fact that the field energy density is given by ##u_g = \frac{-1}{8\pi G}g^2##.
Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give ##U = \iiint \frac{GM^2}{8 \pi r^4} dv = \frac{-GM^2}{2R}##.
Is my solution correct?
Now, ##g = \frac{Gm}{r^2}## in this case and substituting gives ##u_g = \frac{-GM^2}{8 \pi r^4}##. Integrating this over volume will give ##U = \iiint \frac{GM^2}{8 \pi r^4} dv = \frac{-GM^2}{2R}##.
Is my solution correct?