92-94] Electrified Soap-Bubble 81 



so that the force on the conducting surface would be only about ^^ of an 

 atmosphere : say '3 mm. of mercury. 



If a gold-leaf is beaten so thin that 1 gm. occupies 1 sq. metre of area, 

 the weight of this is '0981 dyne per sq. cm. In order that 27ro- 2 may be 

 equal to '0981, we must have a = '1249. Thus a small piece of gold-leaf 

 would be lifted up from a charged surface on which it rested as soon as the 

 surface acquired a charge of about J of a unit per sq. cm. 



Electrified Soap-Bubble. 



94. As has already been said, this mechanical force shews itself well on 

 electrifying a soap-bubble. 



Let us first suppose a closed soap-bubble blown, of radius ft. If the 

 atmospheric pressure is II, the pressure inside will be somewhat greater than 

 II, the resulting outward force being just balanced by the tension of the 

 surface of the bubble. If, however, the bubble is electrified there will be an 

 additional force acting normally outwards on the surface of the bubble, namely 

 the force of amount 27r<r 2 per unit area just investigated, and the bubble will 

 expand until equilibrium is reached between this and the other forces acting 

 on the surface. 



As the electrification and consequently the radius change, the pressure 

 inside will vary inversely as the volume, and therefore inversely as ft 3 . Let 



\ 



FIG. 37. 



us, then, suppose the pressure to be KJO?. Consider the equilibrium of the 

 small element of surface cut off by a circular cone through the centre, of small 

 semi-vertical angle 6. This element is a circle of radius ft#, and therefore 

 of area 7rft 2 2 . The forces acting are : 



(i) The atmospheric pressure n?rft 2 ^ 2 normally inwards. 



(ii) The internal pressure 7rft 2 2 normally outwards. 



ft 



j. 6 



