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## Main Question or Discussion Point

We define the position of the centre of mass of a system of ##n## masses as:

$$\vec{r_{cm}} = \frac{\sum_{i=1}^n m_i \vec{r_i}}{\sum_{i=1}^n m_i}$$

Why is there no such thing as "centre of charge", defined for ##n## point charges:

$$\vec{r_{cq}} = \frac{\sum_{i=1}^n q_i \vec{r_i}}{\sum_{i=1}^n q_i}$$

$$\vec{r_{cm}} = \frac{\sum_{i=1}^n m_i \vec{r_i}}{\sum_{i=1}^n m_i}$$

Why is there no such thing as "centre of charge", defined for ##n## point charges:

$$\vec{r_{cq}} = \frac{\sum_{i=1}^n q_i \vec{r_i}}{\sum_{i=1}^n q_i}$$