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Let V be a bounded region of space and let ø be an electrostatic potential that is source free in this region, so that V²ø = 0 throughout V. Suppose that for all a lying on the boundary S = av, we have ø(T) = –f(F)n · Vó(F) where f is a positive function (f(ã) > 0) and în is the outward pointing normal. Show that O = 0 throughout V.

Let V be a bounded region of space and let ø be an electrostatic potential that is source free in this region, so that V²ø = 0 throughout V. Suppose that for all a lying on the boundary S = av, we have ø(T) = –f(F)n · Vó(F) where f is a positive function (f(ã) > 0) and în is the outward pointing normal. Show that O = 0 throughout V.

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Let V be a bounded region of space and let ø be an electrostatic potential that is source free in this region, so that V²ø = 0 throughout V. Suppose that for all ở lying on the boundary S = av, we have ø(F) = –f(F)î · Vo(f) where ƒ is a positive function (f(7) > 0) and în is the outward pointing normal. Show that $ = 0 throughout V.
Transcribed Image Text:Let V be a bounded region of space and let ø be an electrostatic potential that is source free in this region, so that V²ø = 0 throughout V. Suppose that for all ở lying on the boundary S = av, we have ø(F) = –f(F)î · Vo(f) where ƒ is a positive function (f(7) > 0) and în is the outward pointing normal. Show that $ = 0 throughout V.
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