3. The diagram below shows the initial charge and position of three metal spheres, X, Y, & Z. +12 Y Sphere X is brought into contact with sphere Y and then removed. Then sphere Y is brought into contact with sphere Z and removed. What is the charge on each sphere after this procedure is completed? Show your work. 4. If all three spheres of the above question were brought together, and then moved apart at the same time, what would the charge on each be? 5. What would your answer to the previous question have been if the three spheres were insulators, not metal conductors?

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For each scenario below, there are four identical balls, A, B, C, and D, which conduct, and ball A starts with a charge of +Q, while B, C, and D have zero net charge. The balls are then touched to each other and separated as described below. Assume that any balls not in contact are placed very far away. For each scenario, find the final charge of ball D as a whole number fraction of Q. For example, if the final charge of ball D is Q/5, enter "1" in the numerator and "5" in the denominator. Remember, before each scenario begins, balls A, B, C, and D have set up to have charges of +Q, 0, 0, and 0, respectively. Scenario 1: A and B touch and are separated, then A and C touch and are separated, then A and D touch and are separated. QD x Q Scenario 2: A and B touch and are separated, then B and C touch and are separated, then C and D touch and are separated. QD XQ Scenario 3: A and D touch and are separated, then D and C touch and are separated, then D and A touch and are separated, then A…

The diagram below shows a positive point charge placed near a neutral metal cube. The location marked with a × can be ignored. a. Draw the charge distribution within the metal cube and reduce it to an “effective point charge model, as shown in class.b. Is the positive point charge attracted to, repelled by, or unaffected by the metal cube? Please explain using a neat vector diagram to support your arguments.c. In a second identical experiment, the positive point charge +q is replaced by a negative point charge −q. Does a negative point charge interact differently with the metal cube as compared to the positive point charge? Briefly explain your reasoning.