Question

The figure shows eight-point charges arranged at the corners of a cube with sides of length d. The values of the charges are +q and -q,as shown . This is a model of one cell of a cubic ionic crystal. In sodium chloride (NaCl),for instance,the positive ions are $N{a}^{+}$ and the negative ions are $C{l}^{-}$ .Calculate the potential energy Uof this arrangement.(Take as zero the potential energy of the eight charges when they are infinityly far apart.)

• A. $\frac{3q^2}{\pi {\epsilon }_{0}d}\left(1-\frac{1}{\sqrt{2}}+\frac{1}{3\sqrt{3}}\right)$
• B. $-\frac{3q^2}{\pi {\epsilon }_{0}d}\left(1-\frac{1}{\sqrt{2}}+\frac{1}{3\sqrt{3}}\right)$
• C. $\frac{q^2}{12\pi {\epsilon }_{0}d}\left(1-\frac{1}{\sqrt{2}}+\frac{1}{3\sqrt{3}}\right)$
• D. $\frac{-q^2}{12\pi {\epsilon }_{0}d}\left(1-\frac{1}{\sqrt{2}}+\frac{1}{3\sqrt{3}}\right)$

Answer 1

The correct option is C $\frac{q^2}{12\pi {\epsilon }_{0}d}\left(1-\frac{1}{\sqrt{2}}+\frac{1}{3\sqrt{3}}\right)$

Like poles repel to each other and unlike poles attracts each other.

Hence $\frac{q^2}{12\pi {ϵ}_{0}d}(1-\frac{1}{\sqrt{2}}+\frac{1}{3\sqrt{3}})$