Question

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 $\mathrm{P} 19.78$.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 $-\rho .$ )

          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 $\mathrm{P} 19.78$.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 $-\rho .$ )

Added by Willie N.

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