Answer to Question #100371 in Physics for Kishwer
Find the electric field produced by a uniformly polarized sphere of radius R
1
2019-12-13T10:08:47-0500
The potential outside:
"V(r)=\\frac{P}{3\\epsilon_0}\\frac{R^3}{r^2}\\cos\\theta=\\frac{1}{4\\pi \\epsilon_0}\\frac{\\frac{4\\pi PR^3}{3}}{r^2}\\cos\\theta"
"V(r)=\\frac{1}{4\\pi \\epsilon_0}\\frac{\\bold{p\\cdot \\hat{r}}}{r^2}" where
"p=\\frac{4\\pi PR^3}{3}" The potential inside:
"V(r)=\\frac{p}{3\\epsilon_0}r\\cos\\theta=\\frac{p}{3\\epsilon_0}z" The electric field:
"\\bold{E}=-\\nabla V=-\\frac{P}{3\\epsilon_0}\\hat{\\bold{z}}"
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