OpenStax College Physics for AP® Courses, Chapter 18, Problem 12 (Test Prep for AP® Courses)

This is College Physics Answers with Shaun Dychko. Since students have an uncharged metal sphere and they want to give that sphere the same charge as a charged aluminum pie plate so which of the following would give the sphere a net charge that's the same as the pie plate? So in... (well, I guess I got the answer (d) selected) touching the pie plate to the metal sphere is the answer because then the charge would distribute itself evenly among both pie plate and metal sphere and then result in that charge to be on the sphere but I will talk about these other options too just for interest. So but to draw scenario (d) after the sphere and the pie plate, which in two dimensions both look like circles, are touching, they will have an even distribution of charge— let's suppose it's a positive charge— and then when you separate them afterwards, you will be left with the sphere charged— the same as the pie plate was; the magnitude of the charge on the pie plate will be reduced but the sign of it will be the same. Okay! And that was the question here: is the same sign of charge not the same magnitude of charge? Okay! So this is option (d), it's the answer and this drawing illustrates why but suppose we wanted to consider option (a) bringing the pie plate close to but not touching the metal sphere and then moving the pie plate away what will happen there is when the pie plate is close to the neutral sphere, it will induce a charge distribution in this sphere so here's the pie plate— P for 'pie plate' and S for 'sphere'— the pie plate is positively charged suppose and the neutral sphere will have an induced distribution of charge when the pie plate is close and actually, it will be the other way around though it will have negative charges close to the pie plate and the positive charges away and then once the pie plate is separated from the sphere, this sphere will eventually return back to just regular neutral sphere and this distribution will become just evenly distributed among the whole sphere and there won't be any polarity to the sphere. Okay! Part (b) pie plate close to but not touching the sphere then momentarily touching a grounding wire to the sphere. So that's an interesting suggestion and so we will have this distribution in this sphere when the pie plate is close and then when the grounding wire is touched then this excess positive charge will go down the grounding wire or if you prefer since positive charges don't actually move, negative charges will be sucked up from the ground to neutralize these positive charges and you will end up having the sphere all negatively charged. And then when the pie plate is taken away then this sphere will be left negatively charged. Okay! And so this would be a charge of the opposite sign of the pie plate, which is why (b) is not the answer and then in (c), the pie plate is close to but not touching the sphere and then put a grounding wire on the pie plate, it will just make both things neutral in that case and so there will be no charge at all on either object. Okay so the answer is (d).