Question 4.13: Two dipoles with dipole moments -5 az nC·m and 9 az nC·m are...

V=\sum\limits_{k=1}^{2}\frac{p_{k}\cdot r_{k}}{4\pi\varepsilon_{o}r^{3}_{k}}=\frac{1}{4\pi\varepsilon_{o}}\left[\frac{p_{1}\cdot r_{1}}{r^{3}_{1}}+\frac{p_{2}\cdot r_{2}}{r^{3}_{2}} \right]

where

p_{1}=-5a_{z},      r_{1}=\left(0,0,0\right)-\left(0,0,-2\right)=2a_{z},      r_{1}=\left|r_{1}\right|=2

p_{2}=9a_{z},      r_{2}=\left(0,0,0\right)-\left(0,0,3\right)=-3a_{z},      r_{2}=\left|r_{2}\right|=3

Hence

V=\frac{1}{4\pi\cdot \frac{10^{-9}}{36\pi} } \left[\frac{-10}{2^{3}}-\frac{27}{3^{3}} \right] \cdot 10^{-9}=-20.25V