The centre of mass is defined as R =1 M _im_i r_ i . Suppose we d… - Vidyadip

Question

The centre of mass is defined as $\overrightarrow{\text{R}}=\frac{1}{\text{M}}\sum\limits_\text{i}\text{m}_\text{i}\overrightarrow{\text{r}_{\text{i}}}.$ Suppose we define "centre of charge" as $\overrightarrow{\text{R}}_\text{c}=\frac{1}{\text{Q}}\sum\limits_\text{i}\text{q}_\text{i}\overrightarrow{\text{r}_{\text{i}}}$ where $q_i$ represents the $i^{th}$ charge placed at $\overrightarrow{\text{r}_\text{i}}$ and Q is the total charge of the system.

Can the centre of charge of a two-charge system be outside the line segment joining the charges?
If all the charges of a system are in X-Y plane, is it necessary that the centre of charge be in X-Y plane?
If all the charges of a system lie in a cube, is it necessary that the centre of charge be in the cube?

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Answer

Center of charge can lie away from line segment joining two charges in case both charges are unequal and are of same charge. but eventually would lie on the axis joining two charges.
Yes in case all charge particles are in same plane the center of charge would lie on same plane.
Yes in case all charges are in cube in that case center of charge would lie on the same cube.

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