Electromagnetism / Electrodynamics I · Fields in matter and polarization
Radial polarization produces a compensating shell charge
Problem
A dielectric sphere of radius $R$ has $\mathbf P=kr\hat{\mathbf r}$ for $r<R$ and zero outside, where $k$ is constant. Find $\rho_b$, the surface density at $r=R$, and the total bound charge from each contribution.
Hint
Apply the spherical divergence formula to $f(r)=kr$.
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