(a) An insulating sphere with radius has a uniform charge
Chapter 22, Problem 22.61(choose chapter or problem)
(a) An insulating sphere with radius a has a uniform charge density \(\rho\). The sphere is not centered at the origin but at \(\vec{r}=\vec{b}\) Show that the electric field inside the sphere is given by \(\vec{\boldsymbol{E}}=\rho(\vec{r}-\vec{b}) / 3 \epsilon_{0}\). (b) An insulating sphere of radius R has a spherical hole of radius a located within its volume and centered a distance b from the center of the sphere, where a < b < R (a cross section of the sphere is shown in Fig. P22.61). The solid part of the sphere has a uniform volume charge density \(\rho\). Find the magnitude and direction of the electric field \(\vec{E}\) inside the hole, and show that \(\vec{E}\) is uniform over the entire hole. [Hint: Use the principle of superposition and the result of part (a).]
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