HW-571-6 - ϕ and(b the charge Q induced on the boss Hint...

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1 Phys 571 , Fall 2010 Assignment #6 Due: Nov 10th, 2010 1. Using the method of images, discuss the problem of a point charge q inside a hollow, grounded, conducting sphere of inner radius a . Find (a) the potential inside the sphere; (b) the induced surface-charge density; (c) the magnitude and direction of the force acting on q . (d) Is there any change in the solution if the sphere is kept at a fixed potential V ? If the sphere has total charge Q on its inner and outer surfaces? 2. A grounded conducting plane has a hemispherical boss of radius a . Center of the boss lies on the plane. A charge q is located on the symmetry axes at a distance b > a from the plane (see figure). Using the method of images find (a) the potential
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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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