IDEA OF POTENTIAL. 191 



in. Fortescue's design again. There is a constant potential 

 difference between successive tinfoil cylinders in Fig. 129, and a 

 constant potential difference between successive tinfoil cylinders 

 is to be provided for in Fig. 130 as explained later; but if the 

 potentials of the edges of the tinfoil cylinders in Fig. 130 are 

 to be conformable to the uniform electric field which is repre- 

 sented by the coarse lines of force in Fig. 130 it is necessary to 

 terminate the cylinders along the dotted straight lines as shown. 

 With this arrangement, however, the tinfoil cylinders do not 

 all have the same area and they do not automatically adjust 

 themselves to equal potential differences as explained in Art. 89. 

 Therefore to provide for equal potential differences between 

 successive tinfoil cylinders in Fig. 130 it is necessary to connect 

 the successive cylinders to proper points in the winding of the 

 transformer (the bushing in Figs. 129 and 130 being used to 

 insulate the wires which pass through a metal case to the high- 

 voltage windings of a transformer). 



PROBLEMS. 



1. All space is filled with a fluid moving parallel to the #-axis 

 of reference at a uniform velocity of 10 centimeters per second. 

 Find an expression for the velocity potential of the fluid. Ans. 

 IQJC + any constant. 



2. Derive an expression for the electric potential of a uniform 

 electric field which is parallel to the x-axis of reference and of 

 which the intensity is 1,000 volts per centimeter. Ans. i,ooo# 

 + any constant. 



3. The entire region throughout a room is a uniform electric 

 field directed vertically upwards and its intensity is 2,000 volts 

 per centimeter, (a) Choosing the floor as the region of zero 

 potential, what is the potential at a point 150 centimeters above 

 the floor? (b) What kind of lines are the lines of force, straight 

 or curved, and in what direction? (c) What kind of surfaces 

 are the surfaces of equipotential, plane or curved, and in what 

 direction do these surfaces lie? Ans. (a) 300,000 volts, (b) 



