54 



ADVANCED ELECTRICITY AND MAGNETISM. 



is done on a body is equal to 



dW 

 dt ' 

 have: 



-j, as above explained, we 



dW dl 



dt ~ LI dt 



(i) 



The kinetic energy of a body 

 which is moving at velocity / 



W = I/2LP (3) 



where L is the mass of the 

 body. This equation may be 

 established as follows: 



Integrating equation (i), we 

 have: 



W = i /2LP+ a constant (5) 

 but we are here concerned with 

 the energy which depends upon 

 /, and which is zero when / is 

 zero. The constant term in 

 equation (5) therefore disap- 

 pears and equation (5) reduces 

 to equation (3). 



36. The starting of a boat. 



At a certain instant a con- 

 stant force E begins to act on 

 a boat, and it is required to find 

 an algebraic expression for the 

 increasing velocity i of the 

 boat, on the assumption that 

 the frictional drag of the water 

 is .exactly proportional to i, 

 or equal to Ri. 



that the rate at which work is 

 done on a circuit is equal to 



dW 



, as above explained, we 



have: 



dW dl 



dt ~ L1 dt 



(2) 



The kinetic energy of a circuit 

 in which a current / is flowing 

 is: 



W = I/2LP (4) 



where L is the inductance of 

 the circuit. This equation may 

 be established as follows: 



Integrating equation (2), we 

 have: 



W= 1/2 ZJ 2 + a constant (6) 

 but we are here concerned with 

 the energy which depends on 

 /, and which is zero when / is 

 zero. The constant term in 

 equation (6) therefore disap- 

 pears and equation (6) reduces 

 to equation (4). 



Growth of current in a circuit. 

 At a certain instant a con- 

 stant electromotive force E 

 begins to act on a circuit, and 

 it is required to find an alge- 

 braic expression for the grow- 

 ing current i. 



