Unformatted text preview: ϕ , and (b) the charge Q induced on the boss. Hint: use three image charges. q 3. Consider a potential problem in the half-space deﬁned by z ≥ 0, with Dirichlet boundary conditions on the plane z = 0 (and at inﬁnity) (a) Write down the appropriate Green’s function G ( r , r ). (b) If the potential on the plane z = 0 is speciﬁed to be ϕ = V inside a circle of radius a centered at the origin, and ϕ = 0 outside that circle, ﬁnd an integral expression for the potential at the point P speciﬁed in terms of the cylindrical coordinates ρ,φ,z . (c) Show, that along the axis of the circle ρ = 0, the potential is given by ϕ = V ± 1-z √ a 2 + z 2 ²...
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- Fall '10
- Charge, Method acting, Euclidean geometry, Archimedes, Dirichlet boundary conditions