In table salt-sodium chloride, \(\mathrm{NaCl}-\) the \(\mathrm{Na}^{+}\)and \(\mathrm{Cl}^{-}\) ions are arranged in a cubic crystal structure. You can observe in this structure a cube made up of eight ions: four \(\mathrm{Na}^{+}\)and four \(\mathrm{Cl}^{-}\)in alternating corners. Each \(\mathrm{Na}^{+}\) has a radius of \(99 \mathrm{pm}\), each \(\mathrm{Cl}^{-}\)has a radius of \(181 \mathrm{pm}\), and the ions are spaced as though they were solid balls of these sizes, touching their neighbors.

(a) For a single cube of this arrangement, what are the magnitude and direction of the electric field at one of the \(\mathrm{Na}^{+}\)ions due to the other seven ions in the cube?

(b) What are the magnitude and direction of the vector sum of the electric forces exerted on this \(\mathrm{Na}^{+}\)ion by the other seven ions?