A square rectangular pipe (sides of length a) runs parallel to the z-axis (from - to...

 

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A square rectangular pipe (sides of length a) runs parallel to the z-axis (from - to +o). V-V. (constant) on this surface y V-0 on this surface on this surface The 4 sides are maintained with boundary conditions given in the figure. Each of the 4 sides is insulated from the others at the corners. The "three stripe symbol" on the left of the figure means that this side a grounded conductor. a) Find the potential V(x, y, z) at all points in this pipe. Use the method of separation of variables, following the same steps as we took in the lecture for a similar problem. b) What does the boundary condition on the bottom wall mean? Is the bottom wall a conductor? c) Find the charge density o(r = 0, y, z) everywhere on the left conducting wall (r = 0). A square rectangular pipe (sides of length a) runs parallel to the z-axis (from - to +o). V-V. (constant) on this surface y V-0 on this surface on this surface The 4 sides are maintained with boundary conditions given in the figure. Each of the 4 sides is insulated from the others at the corners. The "three stripe symbol" on the left of the figure means that this side a grounded conductor. a) Find the potential V(x, y, z) at all points in this pipe. Use the method of separation of variables, following the same steps as we took in the lecture for a similar problem. b) What does the boundary condition on the bottom wall mean? Is the bottom wall a conductor? c) Find the charge density o(r = 0, y, z) everywhere on the left conducting wall (r = 0).