# HW-6 - HW-6 1 A rectangular pipe running parallel to the z...

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Unformatted text preview: HW-6 1. A rectangular pipe, running parallel to the z axis (from -∞ to +∞), has three ground metal sides at y=0, y=a, and x=0. The fourth side, at x=b, is maintained at a specific potential V0(y). (a) Develop a general formula for the potential within the pipe. (b) Find the potential explicitly for the case of V0(y)= V0 (constant). 2. A cubical box (side length of a) consists of five metal plates (x=0, x=a, y=0, y=a, and z=0), which are welded together and grounded. The top (z=a) is made of a separate sheet of metal, insulated from the others, and held at a constant potential V0. Find the potential inside the box. 3. Find the potential outside a charged metal sphere (Charge Q, radius R) placed in an otherwise uniform electric field E0. 4. Four charged particles are placed as shown in the figure. Find a simple approximation for the potential far away from the origin. (Express your answer in spherical coordinates.) 5. For a spherical shell of radius R with a surface charge k cos . (a) Calculate the dipole moment of this charge distribution. (b) Find the approximate potential, at points far away from the sphere, and compare the exact kR3 cos V ( r , ) result 3 0 r 2 . What can you conclude about the higher multipoles? ...
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