Question
A solid sphere of radius $R$ has a nonuniform charge distribution $\rho=A r^{2},$ where $A$ is a constant. Determine the total charge, $Q$, within the volume of the sphere.
Step 1
This is given by the integral over the entirety of the sphere of the charge distribution $\rho$ times the volume element $dV$. In spherical coordinates, this becomes: \[Q = \int \rho dV = \int_0^R \int_0^\pi \int_0^{2\pi} \rho(r) r^2 \sin\theta d\phi d\theta dr\] Show more…
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