138-141] Boundary Conditions 125 



The lines of force will be straight, except for those which pass near to the 

 edge of the dielectric slab. Neglecting a small correction required by the 

 curvature of these lines, the capacity C of the condenser is given by 



c _ B A-B 



' 



A 



4>7rd ' , f , /, 1 



ktrdld- 1 --r 



( V 



a quantity which increases as B increases. If V is the potential difference 

 and E the charge, the electrical energy 



If we keep the charge constant, the electrical energy increases as the 

 slab is withdrawn. There must therefore be a mechanical force tending to 

 resist withdrawal : the slab of dielectric will be sucked in between the plates 

 of the condenser. This, as will be seen later, is a particular case of a general 

 theorem that any piece of dielectric is acted on by forces which tend to 

 drag it from the weaker to the stronger parts of an electric field of force. 



Charge on the Surface of a Dielectric. 



140. Let dS be any small area of a surface which separates two media 

 of inductive capacities K 1} K 2 , and let this bounding surface have a charge of 

 electricity, the surface density over dS being a. If we apply 

 Gauss' Theorem to a small cylinder circumscribing dS we obtain 



o 



where in either medium denotes differentiation with respect 

 dv 



to the normal drawn away from dS into the dielectric. 



141. As we have seen, the surface of a dielectric may be 

 charged by friction. A more interesting way is by utilising FIG. 45. 

 the conducting powers of a flame. 



Let us place a charge e in front of a slab of dielectric as in fig. 43. 

 A flame issuing from a metal lamp held in the hand may be regarded as 

 a conductor at potential zero. On allowing the flame to play over the 

 surface of the dielectric, this surface is reduced to potential zero, and the 

 distribution of the lines of force is now exactly the same as if the face of 

 the dielectric were replaced by a conducting plane at potential zero. The 



