Dielectric Sphere Fields
A central slice through a dielectric sphere placed in a uniform electric field, with the sphere permittivity varied relative to the surrounding medium.
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β = (εs - εm) / (εs + 2εm)
Vout = -E0 r cosθ + E0a3β cosθ/r2
Vin = -[3εm/(εs+2εm)] E0 r cosθ
E = -grad V, Dn and Et are continuous at r = a
Vout = -E0 r cosθ + E0a3β cosθ/r2
Vin = -[3εm/(εs+2εm)] E0 r cosθ
E = -grad V, Dn and Et are continuous at r = a