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5.4.10: Bubble Inside a Uniform Solid Sphere

Last updated

Mar 5, 2022
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- 5.4.9: Solid Sphere
- 5.5: Gauss's Theorem

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Figure 5.11.png
$\text{FIGURE V.11}$

$\text{P}$ is a point inside the bubble. The field at $\text{P}$ is equal to the field due to the entire sphere minus the field due to the missing mass of the bubble. That is, it is

$\textbf{g} = -\frac{4}{3} \pi G ρ \textbf{r}_1 - (-\frac{4}{3} \pi G ρ \textbf{r}_2) = -\frac{4}{3} \pi G ρ ( \textbf{r}_1 - \textbf{r}_2) = -\frac{4}{3} \pi G ρ \textbf{c}. \label{5.4.26} \tag{5.4.26}$

That is, the field at $\text{P}$ is uniform (i.e. is independent of the position of $\text{P}$ ) and is parallel to the line joining the centres of the two spheres.

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