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Could somebody explain the following excerpt from my Physics book? I don’t understand how, if the voltage of the balloon is so high, the charge can be so low? Maybe it’s just worded confusingly:

“Rub a balloon on your hair, and the balloon becomes negatively charged--perhaps to several thousand volts! That would be several thousand joules of energy, if the charge were 1 coulomb. However, 1 coulomb is a fairly respectable amount of charge. The charge on a balloon rubbed on hair is typically much less than a millionth of a coulomb. Therefore, the amount of energy associated w/ the charged balloon is very, very small. a high voltage means a lot of energy only if a lot of charge is involved. Electrical potential energy differs from electric potential (or voltage).”

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Say that you build a charge of 1 $\mu C$ on the balloon rubbing it. A normal rubber balloon has a capacitance of approx 100 pF (spherical capacitor). Thus you have the voltage on the balloon

$C=Q/U$

$U= Q/C = 10^{-6}/10^{-10} = 10000 Volts$

$E = CU^2/2 = 10^{-10}*10^8 =0.01 J$

This is true, when you discharge the balloon a spark happens. This is similar to taking off a sweater when small sparks appear.

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They have exaggerated and created an example that can explain the fact that you cannot get a balloon with $1C$ charge. This is an extremely high charge. The experimental results of charging bodies vary between few $\mu C$ which is equal to $\frac{1}{10^6}C$.

“Rub a balloon on your hair, and the balloon becomes negatively charged--perhaps to several thousand volts! (irony) That would be several thousand joules of energy, if the charge were 1 coulomb. (What I told you $1C$ is a lot.) However, 1 coulomb is a fairly respectable amount of charge. The charge on a balloon rubbed on hair is typically much less than a millionth of a coulomb. ( - the scientific fact with no exaggeration -) Therefore, the amount of energy associated w/ the charged balloon is very, very small. A high voltage means a lot of energy only if a lot of charge is involved. Electrical potential energy differs from electric potential (or voltage).”

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  • $\begingroup$ then where does the large voltage come from? idk, if somebody could just explain a little more in depth what the excerpt is trying to say, i’d really appreciate it. I thoroughly read the chapters of my book on electricity and current, It’s just this little anecdote that isn’t registering. To me it just seems senseless. They just threw it in there and messed me all up haha. $\endgroup$ – Steven Meyers Nov 4 '17 at 17:41
  • $\begingroup$ Look at the update. $\endgroup$ – Sinestro White Nov 5 '17 at 20:27

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