CHAP, x.] ELECTRICITY AND MAGNETISM. 361 



circuit produces a current in the negative direction 

 round the circuit. 



Here we suppose the positive direction along lines-of-force to 

 be the direction along which a free N.-pole would tend to move, 

 and positive direction round the circuit to be the same as the 

 direction in which the hands of a clock move. (See also p. 275.) 



(ii.) The total induced electromotive -force acting 

 round a closed circuit is equal to the rate of 

 decrease in the number of lines -of -force which 

 pass through the circuit. 



Suppose at first the number of lines-of-force passing through 

 the circuit to be N 1? and that after a very short interval of time, 

 /, they are N 3 , then the total induced electromotive-force E is 



E _ Ni-N 2 . 



By Ohm's law, C = E -r- R, therefore 

 r _ Ni-N 2 



~R7~ : 



If N 2 is greater than N 15 and there is an increase in the number 

 of lines-of-force, then N x N 2 will be a negative quantity, and 

 C will have a negative sign, showing that the current is an 

 inverse one. 



A reference to Fig. 134 will make this important law clearer. 

 Suppose ABCD to be a wire circuit of which the piece AB can 

 .slide along DA and CB towards S and T. Let the vertical 

 arrows represent vertical lines of force in a uniform magnetic 

 field, and show (as is the case with the vertical components 

 of the earth's lines-of-force in the northern hemisphere) the 

 direction in which a N. -pointing pole would move if free. The 

 positive direction of these lines of force is therefore vertically 

 downwards through the circuit. Now if AB slide towards ST 

 with a uniform velocity it will cut a certain number of lines-of- 

 force every second, and a certain number will be added during 

 every second of time to the total number passing through the 

 circuit. If N! be the number at the beginning, and N 2 that at 

 the end of a circuit, N t N 2 will be a negative quantity, and 

 there will be an electromotive - force round the circuit whose 

 direction through the sliding piece is from A towards B. 



395. The following adaptation of Ampere's rule to the case 

 of induction may be useful : Suppose a figure swimming in any 

 conductor to turn so as to look along the (positive direction of the] 



