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Electrostatics Tutorials
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EQUILIBRIUM OF A CHARGED SOAP BUBBLE


(i) In equilibrium the air pressure inside a soap bubble is greater than the atmospheric pressure. This excess pressure is produced due to surface tension of the soap solution. If r is the radius of the bubble and T is its surface tension, then for the uncharged bubble in equilibrium

Force due to excess pressure = force produced due to surface tension
pex x pr2 = T(2 x 2pr)
\ pex = (s2 / 2Î0)
(ii) If a bubble is charged, then electrical pressure due to charge acts in outwards direction on the bubble.
pelec = (s2 / 2Î0)
where s is the surface charge density.
(iii) In equilibrium, the force produced due to surface tension is equal to the sum of forces due to excess air pressure inside the bubble and the electrical pressure due to charge, i.e.
(pex + pelec)pr2 = T(2 ◊ 2pr)
Or pex + pelec = (4T/r)
Or pex + (s2/2Î0) = (4T/r)
(iv) For charged bubble,
pex = (4T/r) Ė (s2/2Î0)
(v) If the air pressure inside the bubble is equal to the atmospheric pressure outside, i.e., pex = 0 Then
(s2/2Î0) = (4T/r)
Or
(vi) If charge given to the soap bubble is q, then
s = (q/4pr2)
\ The charge on the bubble
q = 4pe2s

(vii) The intensity of electric field at the surface of the bubble

(viii) The electric potential at the surface of bubble

(ix) On charging a bubble the air pressure inside it decreases because the radius of the bubble increased due to charging.
(x) A soap bubble always expands on giving any kind of charge (positive or negative)


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