A sphere with radius 65 cm has its center at the origin. Equal charges of 2 µC are placed at 72 degree intervals along the equator of the sphere. The Coulomb constant is 8.99×10 N·m^2 / C^2. (a) What is the electric potential at the origin? Answer in units of kV. (b) What is the electric potential at the north pole? Answer in units of kV.
The Attempt at a Solution
The capacitance of an isolated sphere is C = 4*π*ε0*R = (1/K)*R where K = electric constant = 8.99*10^9 N-m²/C². C = 7.23*10^-11 F. The total charge on the sphere is 2*10^-6*(360/72) = 10*10^-6 C. It doesn't matter where the charges are, the conducting sphere will have the same potential at all points on the surface and inside the sphere. V = Q/C = 10*10^-6 / 7.23*10^-11 = 1.38*10^5 V = 138 kV.
The "north pole" would be at the "top" of the sphere, the equator being defined by the location of the charges. Of course, there is no distinction between "top" and "bottom", but it doesn't matter, since the potential is the same everywhere on the sphere. However, my answer got marked wrong for part (b), and I'm not sure why.