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

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                                Part V Theory of Condensers 

Capacity of a Condenser 

(3) The simplest form of condenser consists of a uniform layer of 
insulating matter bounded by two conducting surfaces, and its 
capacity is measured by the quantity of electricity in either surface 
when the difference of potentials is unity 
Let S be the area of either surface, a the thickness of the dielectric 
and k its coefficient of electric elasticity then on one side of the 
condenser the potential is [psi]<sub>1<\sub> and on the other side [psi]<sub>1<\sub> + 1 
and within its substance d[psi]/dx = 1/a = kf (48) 
Since d[psi]/dx and therefore f is zero outside the condenser, the quantity 
of electricity on its first surface = - Sf and on the second + Sf. 
The capacity of the condenser is therefore Sf = S/ak in electromagnetic measure 

Specific Capacity of Electric Induction 

If the dielectric of the condenser be air then its capacity 
in electrostatic measure is S/4[pi]a (neglecting corrections arising 
from the conditions to be fulfilled at the edges. If the dielectric 
have a capacity whose ratio to that of air is D then the capacity 
of the condenser will be DS/4[pi]a 

Hense D = k<sub>0<\sub>/k* where k<sub>0<\sub> is the value of k in air which is 
taken for unity. *49


                            
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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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