hw1remedial.pdf

# hw1remedial.pdf - HW I Remedial homework 1 Laplacians...

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HW I Remedial homework. 1) Laplacians: calculate the Laplacian of the following functions. You can choose which coordinate system to use, but show your work clearly and why you chose such a system. As usual, r is the spherical radius, and ρ the cylindrical radius f ( x, y, z ) = 1 x 2 + y 2 + z 2 + a 2 , f ( x, y, z ) = x 2 + y 2 + z 2 ( x 2 + y 2 + z 2 + a 2 ) 7 / 2 , f ( x, y, z ) = x 2 + y 2 ( z 2 - 2 + ρ 2 ) 1 / 2 , f ( x, y, z ) = ρ ( z 2 - 2 + ρ 2 ) 1 / 2 , 2) Potentials and energy: show all work. A sphere of radius R is centered at the origin and the surface (non-conducting) has a charge Q uniformly distributed on the surface. It is cut by a cone of opening angle α , with vertex at the origin and axis along

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• Fall '15
• Giovani Bonvicini

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