The Problem of the Charged Bubble
Fun physics problem time. I like problems that combine different concepts, so here’s one such from Ye Olde Booke of Cavendish Problems, in a multiple-choice format. It’s not particularly hard, but I like it anyway…
A soap bubble – the film may be taken to be a conductor – of radius 10 mm and surface tension 0.02 N/m is charged by momentarily connecting it to an electrode at 6 kV. How does the radius of the bubble change?
PS. Americans, please note the correct usage of “momentarily”…
Follow @telescoper
In the Dark 
November 21, 2012 at 12:43 pm
Interesting problem! A nice lunchtime teaser.
November 21, 2012 at 2:20 pm
[…] Fun physics problem time. I like problems that combine different concepts, so here’s one such from Ye Olde Booke of Cavendish Problems, in a multiple-choice format. It’s not particularl… […]
November 21, 2012 at 4:16 pm
I am happy to meet someone else who, when the announcement is made at the end of a flight that the airplane will be landing ‘momentarily’, has a picture of wheels touching tarmac, followed by a swift rise back up into the sky….
I reckon the soap bubble will burst.
M.
x
November 21, 2012 at 4:17 pm
Reblogged this on Geeks In Cardiff and commented:
Anyone know? I definitely don’t
November 21, 2012 at 7:15 pm
Dear Mr Coals,
If the charge is from electricity then surely there must be inflation?
Yours sincerely,
Mrs Trellis
November 22, 2012 at 10:51 am
I think I’ll wait until 100 people have voted before revealing the answer…
November 22, 2012 at 5:17 pm
“not particularly hard”. Hmm: not something I’d say of many of the Cavendish problems, and that includes this one. As far as I can see, you have to assemble quite a few ingredients to get an answer – which is why it’s a great problem.
November 22, 2012 at 5:45 pm
Actually, it does have a * next to it now that I look. But I managed to get the right answer quite quickly so I assumed that meant it must be easy…
November 22, 2012 at 7:22 pm
I seem to get one of the supplied numerical answers if I assume an isothermal process, but not if I assume the process is fast enough to be (almost) adiabatic.
November 23, 2012 at 2:13 pm
I thought the same. It’s implicit in the question that you are looking for the long-term static solution – which will be isothermal eventually. But of course what will happen at first (since the charge is deposited ‘momentarily’) is that the bubble will oscillate because the pressure and electrostatic forces are out of balance. You could consider extending the question to ask for the frequency of oscillations, and then the interior of the bubble would have to be treated adiabatically, as with free sound waves.
November 25, 2012 at 4:23 am
I’ll give you the answer momentarily.
Zwicky told me “Always get to the office before the Americans.”
I told him I couldn’t.
November 27, 2012 at 6:43 pm
I got an answer that’s twice as big as anything here, but rather than saying “None of the above” I assumed I’d blown a factor of 2 somewhere.
November 27, 2012 at 6:52 pm
Or possibly a factor of four…
November 27, 2012 at 7:54 pm
That would be twice as surprising as my blowing a factor of 2 — i.e., not very surprising at all.
November 28, 2012 at 10:57 pm
I redid it and got it right this time. I know where one factor of 2 came from; don’t feel like tracking down the other.