486 



THE ELECTROMAGNETIC FIELD. [PT. III. CH. XII. 



In either case, the curve representing the charge as a function of 

 the time has a point of inflexion distant from the origin by the 

 amount 



while the curve of current has one at an equal distance farther on. 

 The curves of charge and of current are represented in Fig. 93. 



Fm. 93. 



CASE II. R* < 4L/K. Both roots complex. If we write 



4Z 2 ' 



= _R L v = /JL 



we have for the roots 



(13) 1 ~^ W> 



7^ = yit - lVt 



and we may write the solution 



(14) q = &* (A cos vt + B sin vt). 



In this case the charge not only dies away, but periodically 

 changes sign, performing a damped harmonic oscillation of the 

 period 



v) cos vt + (Bfi - Av) sin vt}. 



We have for the current 

 06) ,.|-,- 



Determining the constants so that the initial current is zero, and 

 the charge q Q , we have 



(17) q = q e flt (cos vt sin vt] . 



