final200b - PHY 200B Final PHY 200B Winter 2008 Final...

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PHY 200B, Final PHY 200B Winter 2008 - Final - Problem 1. Imagine that a hemisphere of radius R is glued to an infinite plane. The plane is grounded, while the hemisphere is kept at a constant potential V 0 . Determine the potential in the rest of the half-space. Problem 2. Consider a system four charges + q , and four charges q . Put them at the corners of a cube with side 2 a , such that the charges above each other have the same sign, and the charges in the same horizontal plane alternate in sign as you go from corner to corner. What is a) the dipole potential b) the quadrupole potential everywhere in space? Ignore higher multipoles. Now imagine that at a distance L > a from the center of the cube, and parallel to the x y plane, we inserted a thin boundary and change the dielectric constant on the side of the cube to ǫ negationslash = ǫ 0 , while keeping the other side in the vacuum. What are the dipole and quadrupole potentials now, at an arbitrary point in space?
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