80 Conductors and Condensers [CH. in 



The electric intensity at a point near Q and just outside the conductor is 

 47T0-, by Coulomb's Law, and its direction is normally away from the surface. 

 Of this intensity, part arises from the charge on dS itself, and part from the 

 charges on the remainder of the conductor. As regards the first part, which 

 arises from the charge on dS itself, we may notice that when we are con- 

 sidering a point sufficiently close to the surface, the element dS may be 

 treated as an infinite electrified plane, the electrification being of uniform 

 density cr. The intensity arising from the electrification of dS at such a 

 point is accordingly an intensity 2?rcr normally away from the surface. Since 

 the total intensity is 47rcr normally away from the surface, it follows that the 

 intensity arising from the electrification of the parts of the conductor other 

 than dS must also be ZTTCT normally away from the surface. It is the forces 

 composing this intensity which produce the mechanical action on dS. 

 The charge on dS being adS, the total force will be 27ra 2 dS normally away 

 from the surface. Thus per unit area there is a force 2?ro- 2 tending to repel 

 the charge normally away from the surface. The charge is prevented from 

 leaving the surface of the conductor by the action between electricity and 

 matter which has already been explained. Action and reaction being equal 

 and opposite, it follows that there is a mechanical force 27ro- 2 per unit area 

 acting normally outwards on the material surface of the conductor. 



Remembering that R = 47r<7, we find that the mechanical force can also 

 be expressed as - - per unit area. 



07T 



93. Let us try to form some estimate of the magnitude of this mechanical 

 force as compared with other mechanical forces with which we are more 

 familiar. We have already mentioned Maxwell's estimate that a gramme of 

 gold, beaten into a gold-leaf one square metre in area, can hold a charge of 

 60,000 electrostatic units. This gives 3 units per square centimetre as the 

 charge on each face, giving for the intensity at the surface, 



R = 4-77-0- = 38 c.G.s. units, 



and for the mechanical force 



R 2 



27r<7 2 = = 55 dynes per sq. cm. 



OTT 



Lord Kelvin, however, found that air was capable of sustaining a 

 tension of 9600 grains wt. per sq. foot, or about 700 dynes per sq. cm. 

 This gives # = 130, a = 10. 



R 2 

 Taking ^=100 as a large value of R, we find = 400 dynes per 



sq. cm. The pressure of a normal atmosphere is 



1,013,570 dynes per sq. cm., 



