Calculate Electric Potential: Example A conducting sphere of radius R 1 =0.5m is placed at the center of a conducting spherical shell of inner and outer radii of R 2 =0.75m and R 3 =1m. They each carry q 1 =2  C and q 2 =1  C. charges With V=0 at infinity, derive the expression for E(r) and V(r), where r is distance from the center of spheres. Find values for E and V at r=0.4m, 0.7m, 0.8m, and 4m. E =0 & V=0, only if q 1 +q 2 =0. R3R3 R2R2 R1R1 When calculating E & V outside a sphere, the effect of a charged sphere is the same as a point charge located at the center of the sphere

E=0 implies that there are –q 1 on the inner surface of the spherical shell, and q 1 +q 2 on the outer surface. The total charges on the shell = - q 1 +q 1 +q 2 =q 2 Example: Continue E  0 in the interior of a metal in static condition. R3R3 R2R2 R1R1 E = 0 does not mean V=0. Equal potential in the region where E=0

Example: Continue Charge q 2 has no effect on E in this region R3R3 R2R2 R1R1 equal potential sphere since E=0 everywhere in the sphere R3R3 R2R2 R1R1

Example: Shielding charges on the outer surface ( q 1 +q 2 ) will disappear through ground, leaving –q 1 on inner surface. Consequently, E=0 & V=0 in the region 1 (r>R 3 ) R3R3 R2R2 R1R1