The center of mass is defined as Suppose we define “center of charge” as where q i represents the ith charge placed at and Q is the total charge of the system. (a) Can the center of charge of a two-charge system be outside the line segment joining the charges? (b) If all the charges of a system are in X.Y plane, is it necessary that the center of charge be in X-Y plane? (c) If all the charges of a system lie in a cube, is it necessary that the center of charge be in the cube?

Question

Philoid · Accepted Answer

Yes, the center of charge can be outside the line segment joining the charges.

Explanation:

Consider a charge of +q placed at the origin and a second charge of -2q at a distance d from the origin along the X-axis.

The location of center of charge is given by:

.

The center of charge in this case is located at a distance 2d from the origin along the X-axis and it is not in between the line segment joining the charges.

(b) Yes, it is necessary that the center of the charge be in X-Y plane.

Explanation:

Consider a system of three charges lying in the X-Y plane, each with +q C charge. Since they lie in the X-Y plane, their z-component is zero. The z-component of the center of charge is given by

.

So, the center of charge lies in the X-Y plane in this case.

(c) No, it is not necessary.

Explanation:

The location of the center of charge depend on the position of individual charges. It can be shown that if we place the individual charges at specific location inside the charge then the center of charge can lie outside the cube. A somewhat similar case has been presented in part (a) of this question.