Let's say I build up charge on my body by rubbing a balloon on my head so now I am positively charged. Now if I touch a metal object an arc will jump hence discharging the charge I had built up. So for this arc to jump (current) there must have been a potential difference between me and the metal object. So by definition since $V=\frac{W}{q}$ some work must has been done on the electrons when rubbing the balloon on my hair? But specifically, what work have been done on the electrons in this situation?
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2 Answers
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Warning: this answer is speculative in places (where indicated).
As you gain positive charge your potential rises in proportion to the number of electrons lost. [If your body were a sphere of radius a with a uniformly spread surface charge $Q$ the energy stored would be $U= \frac 35 \frac {Q^2}{4\pi \epsilon_0 a}$.] But where does this energy come from?
Energy is needed to remove electrons from your hair. The energy needed per electron is called the work function of your hair. This energy is, I believe, mainly supplied by energy released when the balloon accepts electrons. You could regard this as like a chemical reaction.
I suspect that the rubbing, admittedly involving work done by you, is not the main source of the energy: even though attractive forces will develop between the balloon and your hair as these acquire charges, equal and opposite amounts of work will be done as they approach and recede from each other. The work done rubbing is mainly, I think, work done against friction. Rubbing helps the charge transfer because it increases the effective area of contact between you and the balloon.
answered Feb 10, 2022 at 10:27
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Assuming that you are electrically isolated from the ground otherwise any excess charges on you will leak away to the ground.
Work was done by you when the charged balloon was moved away from your head which had an opposite charge to that on the balloon.
