All Problems

Constant Electric Field in a Vacuum

Problem 3.4

Two positive charges \(q_{1}\) and \(q_{2}\) are located at the points with radius vectors \(\mathbf{r}_ {\mathbf{1}}\) and \(\mathrm{r}_ {2} .\) Find a negative charge \(q_{3}\) and a radius vector \(\mathrm{r}_{3}\) of the point at which it has to be placed for the force acting on each of the three charges to be equal to zero.

Reveal Answer
q3=−q1q2(q1+q2)2,r3=r1q2+r2q1q1+q2q_{3}=-\frac{q_{1} q_{2}}{\left(\sqrt{q_{1}}+\sqrt{q_{2}}\right)^{2}}, \quad \mathbf{r}_{3}=\frac{\mathbf{r}_{1} \sqrt{q_{2}}+\mathbf{r}_{2} \sqrt{q_{1}}}{\sqrt{q_{1}}+\sqrt{q_{2}}}
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