 #1
cwill53
 215
 40
 Homework Statement:

Two positive ions and one negative ion are fixed at the vertices of
an equilateral triangle. Where can a fourth ion be placed, along the
symmetry axis of the setup, so that the force on it will be zero? Is
there more than one such place? You will need to solve something
numerically.
 Relevant Equations:
 $$\vec{F}=\frac{1}{4\pi \varepsilon _0}\sum_{j=1}^{N}\frac{q_0q_j\hat{r}_{oj}}{r^{2}_{oj}}$$
I'm not really sure where to start with this problem, but I wanted to ask a few questions about the approach I should use.
Is it reasonable to say that a gradient could be set up that could describe the force on the fourth ion at any point?
The way I'm thinking of this problem is, I want to find how the sum of the forces on the fourth ion change as the fourth ion moves through space.
But I'm not sure if this is the correct way to think about it or how to solve this mathematically.
Is it reasonable to say that a gradient could be set up that could describe the force on the fourth ion at any point?
The way I'm thinking of this problem is, I want to find how the sum of the forces on the fourth ion change as the fourth ion moves through space.
But I'm not sure if this is the correct way to think about it or how to solve this mathematically.
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