PHYS 3 Chapter Notes - Chapter 22.4-22.5: Gaussian Surface, Surface Charge, Electric Field

The potential at the surface of a sphere is given by V(theta)=kcos(4theta) Find the potential inside and outside the sphere. Find the electric field inside and outside the sphere. Find the surface charge density sigma(theta) on the sphere. A spherical conductor of radius R and charge Q is surrounded by a spherical dielectric material of dielectric constant K and radius 2R. A thin conducting shell that has charge -2Q surrounds the dielectric material, Use Gauss's Law to find the electric field in each region (r 2R). Find the electric potential in cach region and the energy stored in the system. A thin dielectric rod of cross sectional area A extends along the x-axis from x = 0 to x = L. The polarization of the rod is along its length, and is given by Px = ax2 + b. Find the surface bound charge density (sigmab) and volume bound charge density (rhob). Show explicitly that the total polarization charge vanishes. Four charges are arranged in a linear array. The charge -3q is placed at the origin and three charges, each +q, are placed at (0,0,a),(0, -a, 0).and (0,a,0). Find the two leading terms for the potential V which is valid for