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The center of mass is defined as R=(1/M)Σimiri. Suppose we define "center of charge" as Rc =(1/Q)Σiqiri where qi represents the ith charge placed at ri 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? |
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Answer» (a) Yes. Because the charges are of two different type, positive and negative, unlike mass which is all similar type. For example, suppose that there is 2q charge at the origin and -q at 2 units along the x-axis. Its center of charge will be at a distance = {1/(-q+2q)}*(-q*2+2q*0) =-2q/q =-2. Clearly, the center of charge, in this case, lies outside the line segment joining the two charges. (b) Since the z-coordinate of all the charges, in this case, is zero so Σiqizi =0. Hence z-coordinate of center of charge =(1/Q)Σiqizi =0. It means the center of charge necessarily lies in X-Y plane. (c) No. As we have seen in (a) that center of charge of two charges may lie outside the line segment joining the two charges, hence the center of charge, in this case, may lie outside the cube. |
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