UPPSC 2019 Prelims GS Paper-I · Question 12 of 150

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.

• (b)Its radius decreases — 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)The bubble collapses — 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)None of the above — A definite, predictable and observable change does occur — the bubble expands — so 'none of the above' is ruled out by option (a) being right.

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.

The trap is the everyday intuition that 'charge' means attraction and hence contraction. Remember that a single isolated charged body carries only ONE sign of charge, and like charges repel — so the effect on the body itself is always to push it apart. Note also that the result does not depend on whether the charge is positive or negative, because the electrostatic pressure goes as sigma-squared. If you prefer an energy argument: adding charge adds electrostatic energy that falls as the bubble gets bigger, so the system lowers its total energy by expanding.

• Excess pressure inside a soap bubble = 4T/r (two surfaces); inside a liquid drop or an air bubble in a liquid = 2T/r (one surface)
• Charge on a conductor resides on its surface and, being all of one sign, exerts an outward electrostatic pressure of sigma^2 / 2*epsilon-nought
• Charging therefore reduces the net inward pressure and the bubble expands to a new, larger equilibrium radius
• The result is independent of the sign of the charge, because the electrostatic pressure depends on sigma-squared
• Surface tension is the energy needed per unit area of new liquid surface — it is why free liquid drops take the spherical (minimum-area) shape

• Using 2T/r for a soap bubble — a soap bubble has two surfaces, so it is 4T/r
• Assuming the sign of the charge matters (it does not — electrostatic pressure goes as sigma-squared)
• Thinking charges on the same body attract and shrink it, instead of repelling and expanding it

UPPSC and UPSC ask surface tension as a one-line cause-and-effect question ('why is a drop spherical', 'what happens if a bubble is charged/heated', 'excess pressure formula') — learn 4T/r versus 2T/r and the outward direction of electrostatic pressure and the whole family falls.

• practice — not a real PYQ

  The excess pressure inside a soap bubble of radius r, the surface tension of the soap solution being T, is:

  • (a)T/r
  • (b)2T/r
  • (c)4T/r
  • (d)8T/r

  Answer(c) 4T/r — a soap bubble has two liquid surfaces, so its excess pressure is twice the 2T/r of a single-surface liquid drop.

• practice — not a real PYQ

  Two soap bubbles of unequal size are blown at the two ends of a tube and the connecting tap is opened. What will happen?

  • (a)The smaller bubble grows at the expense of the larger one
  • (b)The larger bubble grows at the expense of the smaller one
  • (c)Both bubbles become equal in size
  • (d)Nothing happens; both remain unchanged

  Answer(b) The larger bubble grows at the expense of the smaller one — excess pressure is 4T/r, so the SMALLER bubble has the HIGHER internal pressure and air flows from it into the bigger bubble.