CHAFrER III 



PROPOSITIONS APPLYING TO 

 44 INVERSE SQUARE" SYSTEMS 



The inverse square law The field Unit quantity Intensity Force 

 between quantities m-^ and m z Lines of force and tubes of force Gauss's 

 theorem If a tube of force starts from a given charge it either continues 

 indefinitely, or if it ends it ends on an equal and opposite charge The 

 product intensity x cross-section is constant along a tube of force Avhich 

 contains no charge If a tube of force passes through a charge and q is 

 the charge within the tube, the product intensity x cross-section changes 

 by lirq The intensity outside a conductor is 4ir<r Representation of 

 intensity by the number of lines of force through unit area perpendicular 

 to the lines Number of lines starting from unit quantity The normal 

 component of the intensity at any surface is equal to the number of 

 lines of force passing through unit area of the surface Fluid displace- 

 ment tubes used to prove the properties of tubes of force Spherical 

 shell uniformly charged Intensity outside the shell Intensity inside 

 the shell Intensity at any point in the axis of a uniformly charged 

 circular disc Intensity due to a very long uniformly charged cylinder 

 near the middle Potential The resolute of the intensity in any 

 direction in terms of potential variation Equipotential surfaces The 

 energy of a system in terms of the charges and potentials The potential 

 due to a uniformly charged sphere at points without and within its 

 surface. 



The inverse square law. In the chapters following this we 

 shall show that certain actions at any point in a space containing 

 electric charges may be calculated on the supposition that each 

 element of charge exerts a direct action at the point proportional 

 to the element, and inversely proportional to the square of the 

 distance of the point from it. The same method of calculation 

 holds for magnetic and for gravitative systems. It is to be noted 

 that the supposition of direct action according to the inverse 

 square law is adopted merely for the purposes of calculation. 

 Experiments show that it gives correct results, but, as we shall 

 see, it does not give us any insight into the real physical actions 

 occurring in the system. 



There are certain propositions which are mathematical conse- 

 quences of the inverse square law, and it will be convenient to 

 prove these before we discuss the experimental verifications. These 

 propositions hold good alike for electric, magnetic, and gravitative 

 systems. 



We shall prove the propositions on the assumption that we are 



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