Question 4.10: Two point charges -4μC and 5μC are located at (2, -1, 3) and...

Let

Q_{1}=-4\mu C,      Q_{2}=5\mu C

V\left(r\right)=\frac{Q_{1}}{4\pi\varepsilon _{o}\left|r-r_{1}\right| } + \frac{Q_{2}}{4\pi\varepsilon _{o}\left|r-r_{2}\right| }+C_{o}

If V\left(\infty\right)=0,C_{o}=0

\left|r-r_{1}\right|=\left|\left(1,0,1\right)-\left(2,-1,3\right) \right|=\left|\left(-1,1,-2\right) \right|=\sqrt{6}

\left|r-r_{2}\right|=\left|\left(1,0,1\right)-\left(0,4,-2\right) \right|=\left|\left(1,-4,3\right) \right|=\sqrt{26}

Hence

V\left(1,0,1\right)=\frac{10^{-6}}{4\pi\times\frac{10^{-9}}{36\pi}}\left[\frac{-4}{\sqrt{6} }+\frac{5}{\sqrt{26}}\right]

=9\times10^{3}\left(-1.633+0.9806\right)= -5.872kV