What happens when some charge is placed on a soap bubble ?

Question

UnlockIAS · Accepted Answer

Correct — A, Its radius increases. An uncharged soap bubble is held in shape by surface tension: because the soap film has two surfaces (inner and outer), the pressure inside exceeds the outside pressure by an excess pressure of 4T/r, where T is the surface tension and r the radius. Now put charge on it. The charge spreads over the surface of the film, and since all of it is of the same sign it repels itself, producing an outward electrostatic pressure of magnitude sigma-squared / 2*epsilon-nought (sigma = surface charge density). That outward push works against the inward pull of surface tension, so the net inward pressure the film can exert falls to (4T/r - sigma^2/2*epsilon-nought). The bubble is no longer in balance at its old size and expands; as r grows, 4T/r falls and sigma falls too (the same charge spread over a bigger area), until a new equilibrium is reached at a LARGER radius. In short, charging a soap bubble behaves like reducing its effective surface tension — the bubble blows itself up a little.

Why the other options are wrong — (b) Shrinking would require some extra inward pressure. The electrostatic pressure on a charged surface always acts outward — a charged surface is pushed out by the field of its own like charges — so charge can never squeeze a bubble smaller.  (c) Collapse is the opposite of what the electrostatic force does. If the charge is pushed to an extreme the bubble eventually bursts because it has expanded and thinned too far — it fails by over-expansion, never by caving inward.  (d) A definite, predictable and observable change does occur — the bubble expands — so 'none of the above' is ruled out by option (a) being right.

Concept: Two standard results meet in this question. First, Laplace's law of excess pressure: a liquid drop or an air bubble inside a liquid has one surface and an excess pressure of 2T/r, while a soap bubble in air has two surfaces and therefore 4T/r. Second, electrostatic pressure: on any charged surface with surface charge density sigma, the outward force per unit area is sigma-squared divided by 2*epsilon-nought. Adding charge to the bubble adds an outward pressure term that partially cancels the inward surface-tension term, so the equilibrium radius moves outward.

State PCS 2019 Q12 — Science & Technology PYQ with Answer

State PCS 2019 Q12 — Science & Technology PYQ with Answer