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Three metal spheres X, Y and Z, are identical in size but carry differing electric charges of –Q, +2Q and -3Q, respectively. The first metal sphere X is brought into contact only with the sphere Y, and then X is brought into contact only with sphere Z. After X makes contact with spheres Y and Z, in the order described, the charge on sphere X is most consistent with which of the following?
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Correct Answer: A. -5/4Q
The basic principle: the spheres are equal in size so when they touch (conduction of charge), the charge will be split equally between the 2 spheres (this is consistent with the Conservation of Charge). When the spheres are separated, each sphere will retain 1/2 of the charge (because they are identical in size).
1) X plus Y: When -Q touches +2Q, the overall charge of the 2 spheres would be -Q + 2Q = +Q but that charge is shared with 2 spheres so each sphere has a +1/2Q charge.
2) new X plus Z: Now +1/2 Q – 3Q = -5/2Q and half of this is -5/4Q
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