8 ELECTRICAL ENGINEERING 



the surface of BC that the potential at every point on it is the 

 same, being the sum of the potentials due to the charge on A and 

 the two charges on BC. 



The same result is illustrated in Fig. 5, which shows the dielec- 

 tric flux produced. 



The flux from A extends out radially in all directions. In the 

 region surrounding BC the lines are deflected and a large number 

 pass. through the conductor BC, since its dielectric constant is 

 infinity and therefore it offers an easy path. For every 4 TT lines 

 entering at B a unit negative charge appears on the surface, 

 and for every 4 ?r lines leaving at C a unit positive charge 

 appears. 



13. Equivalent Charges. A uniformly distributed charge on 

 the surface of a sphere acts as though it were concentrated at the 

 centre. If a sphere of radius R cm. has a charge Q uniformly 



distributed over its surface, the density of the charge is ; 



and since 4?r lines emanate from unit charge, the flux density 

 at the surface of the sphere is ^ = - lines per square centi- 

 meter. If the charge Q is concentrated at the centre of the 

 sphere, then, by formula 3, the flux density at a distance R cm. 



from the charge is -^ and therefore the uniformly distributed 



charge on the surface of the sphere may be represented by an 

 equal charge concentrated at the centre. 



Similarly a uniformly distributed charge on the surface of a 

 cylinder may be represented by an equal charge uniformly dis- 

 tributed along the axis of the cylinder. 



14. Distribution of Potential in the Space Surrounding a 

 Point Charge. In Fig. 6 a positive charge q is placed at the 

 point at an infinite distance from all other charges. The 

 potential at a point PI, distant n cm. from 0, is the work done 

 in moving unit charge from a point of zero potential to the point 

 PI against the forces in the field. The intensity of the force at 

 a distance r cm. from is by formula 



s^p dynes; 



the work done in moving a unit charge against this force through 



