248 Mr. Albert Griffiths : Some 



Since L = M, equations (1) and (2) may be written 



B-^+Lj-L* (3) 



E = ,> 2 + L§-L§ (4) 



The problem is to find how i 2 varies if a break is made in 

 coil (1), i. e. if i\ varies from a finite to a great or infinite 

 value. 



Adding corresponding sides of (3) and (4), 



2E=l>! + 2> 2 ( 5 ) 



Differentiating, 



r, . dr-i , dL . dL //>N 



From (5), 



. 2E-z> 2 

 h • 



From (4), 



,. z> 2 + L$- 2 -E 

 dh_ dt 



dt ~ L 



Substituting these values in (6), 



= L (2E - *> 2 ) J + n V 2 + Lr x 2 § - n'E + W, §• 



The last equation would probably, under any assumption, 

 produce an intractable differential equation. However, the 

 difficulty can be avoided by not troubling about r\ for the 

 present, and assuming that i± varies from a finite value to 

 zero ; later it will be proved that the assumption is consistent 

 with the conditions of the problem, e. g. that the expression 

 deduced for i\ is quite a legitimate one. 



Let 



1 1 — *o ? 

 then 



di • -ict 

 — _ if j p «•»• • 



dt " ° ' 



and on substituting (4) becomes 



di 



dt 

 A solution is 



E = i 2 r 2 + L Tj- H- fcLi e K . 



E /C? L „. n ~-t ,r,\ 



^2= — -rc-^+Ce l (7) 



r 2 r 2 — kL v ' 



