$7.4.37.$ Three charged bodies of the same mass, flying apart, always form an isosceles triangle with angles $\alpha$ at the vertex. The charge of the body located at the top of the triangle is how many times the charge of the body at its base?
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### Solution
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Since the center of mass $G$ of the system remains stationary, the total force $\vec F=\vec F_1+\vec F_2$ on a charge $q$ must be in the same direction as the line joining $G$ and the charge. As the masses of the three charges are the same, $G$ is the geometric centroid of the triangle; that is, $G$ is on the median $AM$ such that $AG=2\cdot MG$. The magnitudes of $\vec F_1$ and $\vec F_2$ are
Let $\angle GBM=\angle BDE=\phi$ (shown in pink) and $\angle GBA=\angle BDC=\theta$ (shown in yellow). Using the law of sines in $\triangle BDE$ and $\triangle BDC$, we have
$7.4.37.$ Three charged bodies of the same mass, flying apart, always form an isosceles triangle with angles $\alpha$ at the vertex. The charge of the body located at the top of the triangle is how many times the charge of the body at its base?
$7.4.37.$ Three charged bodies of the same mass, flying apart, always form an isosceles triangle with angles $\alpha$ at the vertex. The charge of the body located at the top of the triangle is how many times the charge of the body at its base?
@@ -4,7 +4,7 @@Statement
### Solution
### Solution
Since the center of mass $G$ of the system remains stationary, the total force $\vec F=\vec F_1+\vec F_2$ on a charge $q$ must be in the same direction as the line joining $G$ and the charge. As the masses of the three charges are the same, $G$ is the geometric centroid of the triangle; that is, $G$ is on the median $AM$ such that $AG=2\cdot MG$. The magnitudes of $\vec F_1$ and $\vec F_2$ are
Since the center of mass $G$ of the system remains stationary, the total force $\vec F=\vec F_1+\vec F_2$ on a charge $q$ must be in the same direction as the line joining $G$ and the charge. As the masses of the three charges are the same, $G$ is the geometric centroid of the triangle; that is, $G$ is on the median $AM$ such that $AG=2\cdot MG$. The magnitudes of $\vec F_1$ and $\vec F_2$ are
Let $\angle GBM=\angle BDE=\phi$ (shown in pink) and $\angle GBA=\angle BDC=\theta$ (shown in yellow). Using the law of sines in $\triangle BDE$ and $\triangle BDC$, we have
Let $\angle GBM=\angle BDE=\phi$ (shown in pink) and $\angle GBA=\angle BDC=\theta$ (shown in yellow). Using the law of sines in $\triangle BDE$ and $\triangle BDC$, we have
