A sphere of radius $2 a$ is made of a nonconducting material that has a uniform volume charge density $\rho$. (Assume the material does not affect the electric field.) A spherical cavity of radius $a$ is now removed from the sphere as shown in Figure P24.52. Show that the electric field within the cavity is uniform and is given by $E_{x}=0$ and $E_{y}=\rho a / 3 \epsilon_{0} .$ Suggestion: The field within the cavity is the superposition of the field due to the original uncut sphere plus the field due to a sphere the size of the cavity with a uniform negative charge density $-\rho$. Figure $\mathbf{P} 24.52$
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Since the sphere has a uniform volume charge density $\rho$, the electric field within the cavity due to the original uncut sphere is zero. This is because the electric field inside a uniformly charged sphere is zero. Show more…
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