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Induced charge on a conducting sphere in a uniform electric field

A neutral conducting sphere of radius

R

in the field

E z

has exterior potential and induced surface charge

Φ = - E (r - \frac{R ^{3}}{r ^{2}}) cos θ, σ = 3 ϵ_{0} E cos θ .

The surface integral of

σ

is zero.

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Solution