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PhoenixFire
Two point Charges each with a charge of +10nC sit at (0,0,0) and (1,2,1). Find the Electric Field E at point (4,4,4). Give me a second to post my work.
Using Coulombs Law: \[\vec{E}=\frac{kq}{\left| \vec{r} \right|^3}\vec{r}\] Where \(k=\frac{1}{4\pi \epsilon}=9*10^9\) The vector between the point charges and observation point: \[\vec{r_1}=P_1-P_{obs}=<-4,-4,-4>\]\[\vec{r_2}=P_2-P_{obs}=<-3,-2,-3>\] \[\left| \vec{r_1} \right| = \sqrt{48}\]\[\left| \vec{r_2} \right| = \sqrt{22}\] And then basically plugging in the values: \[\vec{E_1}=\frac{9*10*10^{9-9}}{\sqrt{48}^3}\vec{r_1}=<-1.083,-1.083,-1.083>\] \[\vec{E_2}=\frac{9*10*10^{9-9}}{\sqrt{22}^3}\vec{r_2}=<-2.617,-1.744,-2.617>\] And sum them up:\[\vec{E_{tot}}=\vec{E_1}+\vec{E_2}=<-3.7, -2.827, -3.7>\]
Not sure if I am doing it right or not. I have no answers so I can't verify it at the moment.