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I do apologize for the ignorance that I'm sure is imbedded in this question, but I'd like to understand the exact point at which the following argument goes wrong:

1) A battery (let's say an ordinary flashlight battery) maintains a voltage between its positive and negative terminals.

2) The only way to maintain a voltage is by maintaining a charge distribution. Therefore, at least one of the terminals on that battery carries a non-zero net charge.

3) If a terminal carries a non-zero net charge, I ought to be able to use it to pick up a paper clip.

Nevertheless, my flashlight batteries do not pick up paper clips. Is this because the charge is too small or because (at least) one of my three points is dreadfully wrong?

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Your paperclip is electrically neutral. –  Richard Terrett Jul 13 '12 at 0:55
Richard Terrett: Yes, my paper clip is electrically neutral, but I'd have thought that a (say) positively charged terminal would draw electrons toward the close end of the paper clip, whereupon that end would acquire a slight negative charge, leading it to stick to the terminal. –  WillO Jul 13 '12 at 1:03
Richard Terrett: If nevertheless you are saying that I am wrong about point 3), I'd still like to know whether it is true that the terminals on my battery carry non-zero net charges (when, say, the battery is stored in a drawer). –  WillO Jul 13 '12 at 1:04
WillO is right, @Richard is wrong. There will be a surface charge induced on the paper clip to "shield" the inside of the paper clip from the electric field of the battery. And the paper clip will be attracted to the battery terminal. The force must be very small. You can move particles around with static charges, see sciencefair-projects.org/physics-projects/… for example. –  mwengler Jul 13 '12 at 1:38
If there were a charge on the terminals, then opposite terminals from two batteries would attract each other. Part 2 is most likely not correct. –  kbeta Jul 13 '12 at 1:47
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2 Answers

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Richard Terrett's comment gives the correct answer: Richard, you should post it as an answer so people can upvote it.

A battery does indeed have excess charge at it's terminals, and the charge is simply given by the usual equation Q = CV, where C is the capacitance of the battery and V the voltage. However both the capacitance and the voltage of a typical domestic battery are small so the net charge is negligable.

However the reason a battery won't pick up scraps of paper is that the voltage is small. If you do the usual party trick of rubbing a ballon on a pullover you can charge the balloon to several thousand volts. If you only charged the ballon to 1.5V it wouldn't pick up small bits of paper let alone a paperclip.

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@Richard no Richard's answer is not right. The Debye force is an example of how an induced dipole moment (moving + and - charges apart in an on-balance electrically neutral object) allow a neutral object to be attracted to a charge. –  mwengler Jul 13 '12 at 18:10
mwengler: I took John Rennie to mean that you (or perhaps Richard after you corrected him) were right and assumed he'd just mistyped. His answer does indicate that a) a battery does have excess charge at its terminals, b) that excess charge should in principle be able to move a piece of metal but c) the amount of excess charge is in principle too small to move anything the size of a paper clip. I think everyone now agrees on all of this. Yes? –  WillO Jul 13 '12 at 20:14
Yes, I think we're all agreed :-) My point about Richard's comment was that he correctly identified it was the kilovolt potential that allows charged balloons etc to pick up objects. –  John Rennie Jul 14 '12 at 6:16
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Your argument goes wrong at (3). Electric charge repels or attracts electric charge. But an ordinary paper clip is electrically neutral; there are (on average) equal amounts of positive and negative electric charge present so the the net electric force on the paper clip is...?

Edit: My reasoning behind the above only holds true in a uniform electric field as Ron has pointed out to me in the comments. Doh!

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If he is near the positive terminal of the battery, the charge in the charge in the paper clip (which is a conductor) distributes to bring negative charge nearest the positive terminal of the battery and positive charge furthest away from that terminal. Since the force falls off as $1/r^2$ there is a net force of attraction from the neutral paper clip to the battery terminal. But it must be way too small to be noticed. –  mwengler Jul 13 '12 at 1:40
You can still induce a charge distribution in a conductor. If you comb your hair and put the comb near a a slow stream of water from the sink, it will be attracted for this reason. –  kbeta Jul 13 '12 at 1:41
Look, if there is a net field acting on the mobile charges of a conductor, the charges accelerate and redistribute until there is no net field. No net field means no acceleration of the charges, of charge carriers and thus, of the paper clip. –  Alfred Centauri Jul 13 '12 at 2:22
@AlfredCentauri: this is only correct in a homogenous field. When there is no further change in the charge distribution, there is still a force from the gradient of the electric field on the induced dipole, this is the dipole in a field problem, the potential of this force is the dipole moment dotted into the potential gradient. –  Ron Maimon Jul 13 '12 at 3:01
@RonMaimon, very well then, I've profited from this. –  Alfred Centauri Jul 13 '12 at 3:35
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