Il8 ELEMENTS OF ELECTRICITY AND MAGNETISM. 



by the current and remembering that El 

 is equal to the power delivered to the cir- 

 cuit, we have 



P=RI* 



In these equations R may be expressed 

 in ohms, 7 in amperes, E in volts and 

 P in watts, or R may be expressed in 

 abohms, / in abamperes, E in abvolts 

 and P in ergs per second. 



where r is a constant. Then we have 

 F= rv 



Multiplying both members of this equa- 

 tion by v and remembering that Fv is 

 the power that is delivered to the boat, 

 we have 



P=rv l 



In these equations c.g.s. units are most 

 conveniently used, that is, F is expressed 

 in dynes, v in centimeters per second, 

 and P in ergs per second. The coefficient 

 r is exactly analogous to the resistance 

 of an electric circuit. 



Consider the wires on the surface of the cylinder A in Fig. 63 

 with electric currents flowing through them as indicated by the 

 dots and crosses. These wires are pushed sidewise by the mag- 

 netic field, as explained in Art. 51, and, if the cylinder A is 

 allowed to turn so that the wires A move with * this side force, 

 mechanical work is obtained. Where does this work come from ? 

 If the cylinder A is forcibly turned so that the wires move against 

 the side force with which the magnetic field pushes on them, 

 mechanical work is expended. Where does this work go to ? 

 The present chapter is devoted to the consideration of these two 

 questions, and some idea of the conclusions which will be reached 

 may be obtained by a brief discussion of the analogous mechanical 

 problem. A person standing on the swinging span of a draw- 

 bridge as shown in Fig. 8 1 is acted upon by a centrifugal force, as 

 indicated by the arrow, and this centrifugal force depends upon the 

 angular velocity of the moving span. If, while the span is swing- 

 ing, the person walks towards the center of the span, he does work 

 in moving himself against the centrifugal force, and this work helps 

 to turn the span. If the person walks away from the center of the 

 swinging span he is helped by the centrifugal force, or, in other 

 words, he receives energy or work from the swinging span, more 



* A body is said to move with a force which acts upon it when it moves in the 

 direction of the force. A body is said to move against a force which acts upon it 

 when it moves in a direction opposite to the direction of the force. 



