- #1
Chetlin
- 36
- 0
Homework Statement
I have the equation:
[tex]\mathbf{F}_{2,1} = \frac{Q_1 Q_2}{4 \pi \varepsilon_0 {r_{2,1}}^2}\hat{r}_{2,1}[/tex] (standard electric force equation for 2 charges)
I know the value of everything except Q2 and have to find it. The vectors each have 3 components.
Normally in an algebraic equation, I would just solve for a variable by isolating it on one side of the = sign. But this equation involves vectors and I don't think there is a way to divide vectors. I could also subtract F2,1 from both sides which at least gets everything onto one side but I am still left with the vectors. I will effectively have three equations (one for each component of the vectors), but only one variable I have to solve for, right? Does the nature of this problem (it is physical) make it so that only certain vectors are even possible, so if I were to tweak F2,1 and not change the value of anything else, the problem would become impossible to solve because it would represent a physical impossibility?
Homework Equations
Nothing really
The Attempt at a Solution
I used only the x component of each vector and solved it using that equation and got the correct answer. But like I said before, if I tweaked only the y component of F2,1, the equation that used only the x components would be the same (so I'd get the same result) but the entire vector equation would not.