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# hw4 - 1 Phys6103 Homework set#4 1 The Self-Capacitance of a...

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1 Phys6103: Homework set #4 1. The Self-Capacitance of a Non-Spherical Shell The segment from z = c to z = b on the z -axis carries a charge per unit length λ ( z ) = λ 0 a - z a - c , c z b. The point z = a in the ﬁgure below lies on an equipotential surface (dashed) of this charge distribution. This means that ϕ ( x,y,z ) produced by the segment is unchanged if this equipotential surface in vacuum is replaced by a conducting shell with exactly the same shape. Show that the self-capacitance of this shell is C = 2 a - b - c 2 . Note: if you give results in SI system, remember that 4 π² 0 = 1. z b c 0 z z a 2. A Double Layer on a Conducting Sphere A grounded (i.e., having zero potential), conducting, spherical shell of radius R is uniformly coated with polar molecules so that a dipole double layer with τ = τ ˆ r is formed on its surface. Find the potential at every point in space. Does the shell acquire a net charge? 3. The Charge Distribution Induced on a Neutral Sphere

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hw4 - 1 Phys6103 Homework set#4 1 The Self-Capacitance of a...

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