J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’

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                                for estimating the intensity and duration of a current uniform 
while it lasts which would produce the same effects 
(39) Let n<sub>1<\sub> n<sub>2<\s> be the roots of the equation

(LN - M<sup>2<\sup>)n<sup>2<\sup> + (RV + LS)n + RS = 0 

and let the primary coil be acted on by a constant electromotive 
force Rc so that c is the constant current it could maintain 
then the complete solution of the equations for making contact is 

[equations]

From these we obtain for calculating the impulse on the dynamometer 

[equations]

The effects of the current in the secondary coil on the galvanometer 
and dynamometer are the same as those of a uniform current 

- [half]c MR/ RN + LS

for a time 2(L/R + N/S) 

(40) The equation between work and energy may be easily 
verified. The work done by the electromotive force is 

[xi][integral]xdt = c<sup>2<\sup>(Rt - L) 

Work done in overcoming resistance and producing heat = 
R [integral] x<sup>2<\sup>dt + S [integral] y<sup>2<\sup>dt = c<sup>2<\sup>(Rt =3/2 L) 
Energy remaining in the system = [half] c<sup>2<\sup> L 
(41) If the circuit R is suddenly and completely interrupted while carrying 
a current c then the equation of the current in the secondary coil 
would be y = C M/N e<sup>- S/N t<|sup> 
This current begins with a value c M/N and gradually disappears 
The total quantity of electricity is c M/S and the value of [integral]y'<sup>2<\sup> dt is c<sup>2<\sup>M<sup>2<\sup> 2SN 
The effects on the galvanometer and dynamometer are equal to 
those of a uniform current [half] C M/N 
for a time 2 N/S 

The heating effect is therefore greater than that of the current on making cont[act?] 
                            
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Manuscript details

Author
James Clerk Maxwell
Reference
PT/72/7
Series
PT
Date
1864
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J. C. Maxwell’s, ‘Dynamical theory of the electromagnetic field’, 1864. From The Royal Society, PT/72/7

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