Question

two charges -q and -3q are separated by a distance l. these two charges are free to move but do not because there is a third charge nearby. what must be the charge and placement of the charge for the first two to be in equilibrium?

Answer 1

Answer on question #83171, Physics Electric Circuits

two charges -q and -3q are separated by a distance $l$. these two charges are free to move but do not because there is a third charge nearby. what must be the charge and placement of the charge for the first two to be in equilibrium?

Solution

Suppose, that between the negative charges q and 3q is the positive charge $q_x$ and the distance from the charge q to the charge $q_x$ is $l_1$, and the distance from the charge 3q to the charge $q_x$ is $l_2$.

Using Coulomb's law, we draw up and solve a system of equations:

$$\left\{ \begin{array}{l} k \frac{[-q] q_x}{l_1^2} = k \frac{[-q][-3q]}{(l_1 + l_2)^2} \\ k \frac{[-3q] q_x}{l_2^2} = k \frac{[-q][-3q]}{(l_1 + l_2)^2} \end{array} \right\}$$

Hence $l_2 = \sqrt{3} \cdot l_1$; $q_x = 0.4q$

Answer: $l_2 = \sqrt{3} \cdot l_1$; $q_x = 0.4q$

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