A solid metal ball of radius 1.3 cm is located near a hollow plastic ball of radius 2.1 cm bearing a uniformly distributed charge of -4 nC on its outer surface. The distance between the centers of the balls is 10 cm.
Assume the +x axis runs to the right, the +y axis runs up and the +z axis is out.
(a) What is the electric field at the center of the metal ball due only to the charges on the plastic ball?
(b) What is the net electric field at the center of the metal ball?
(c) What is the electric field at the center of the metal ball due only to the charges on the surface of the metal ball?

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.