82 Conductors and Condensers [CH. in 



(iii) The mechanical force due to electrification, 2?r<7 2 x 7ra 2 # 2 normally 

 outwards. 



(iv) The system of tensions acting in the surface of the bubble across 

 the boundary of the element. 



If T is the tension per unit length, the tension across any element of 

 length ds of the small circle will be Tds acting at an angle 6 with the tangent 

 plane at P, the centre of the circle. This may be resolved into Tds cos 6 in 

 the tangent plane, and Tds sin along PO. Combining the forces all round 

 the small circle of circumference 2-7ra0, we find that the components in the 

 tangent plane destroy one another, while those along PO combine into a 

 resultant 27ra# x T sin 6. To a sufficient approximation this may be written 

 as 27ra0 2 T. 



The equation of equilibrium of the element of area is accordingly 



or, simplifying, II - -- 27r<r 2 + = (28). 



Let a De the radius when the bubble is uncharged, and let the radius be 

 ! when the bubble has a charge e, so that 



4-Tra! 2 ' 



Then n ~^ + ^ =0) 



if ^ 2 T 



We can without serious error assume T to be the same in the two cases. 

 If we eliminate T from these two equations, we obtain 



giving the charge in terms of the radii in the charged and uncharged states. 



95. We have seen ( 93) that the maximum pressure on the surface 

 which electrification can produce is only about ^W atmosphere : thus it is 

 not possible for electrification to change the pressure inside by more than 

 about -jJ^o atmosphere, so that the increase in the size of the bubble is 

 necessarily very slight. 



If, however, the bubble is blown on a tube which is open to the air, 

 equation (28) becomes 



T 



7T<7 = - 



a 



