Let n be the normal to an equipotential surface at a point P. The principal radii of curvature of the surface at P are R 1 and R 2 . A formula due to George Green relates normal derivatives (/n n ) of the potential (r) (which satisfies Laplaces equation) at the equipotential surface to the mean curvature
Chapter 7, Problems #2
Let ˆn be the normal to an equipotential surface at a point P. The principal radii of curvature of the surface at P are R1 and R2. A formula due to George Green relates normal derivatives (∂/∂n ≡ ˆn · ∇) of the potential φ(r) (which satisfies Laplace’s equation) at the equipotential surface to the mean curvature of that equipotential surface
Derive Green’s equation by direct manipulation of Laplace’s equation.
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