Lord Kelvin: An account of his scientific life and workGray, Andrew
Science
Lord Kelvin: An account of his scientific life and work
Gray, Andrew
Kelvin, William Thomson, Baron, 1824-1907
If the work done in charging a Leyden jar or electric condenser, by
bringing the charge to the condenser in successive small portions, is
considered, it is at once clear that it must be proportional to the
square of the whole quantity of electricity brought up. For whatever the
charge may be, let it be brought up from a great distance in a large
number N of equal instalments. The larger the whole amount the larger
must each instalment be, and therefore the greater the amount
accumulated on the condenser when any given number of instalments have
been deposited. But the greater any charge that is being brought up, and
also the greater the charge that has already arrived, the greater is
the repulsion that must be overcome in bringing up that instalment, in
simple proportion in each case, and therefore the greater the work done.
Thus the whole work done in bringing up the charge must be proportional
to Q². We suppose it to be ½Q²⧸C, where C is a constant depending on
the condenser and called its capacity.
The idea of the charge as a quantity of some kind of matter, brought up
and placed on the insulated plate of the condenser, has only a
correspondence to the fact, which is that the medium between the plates
is the seat, when the condenser is charged, of a store of energy, which
can only be made available by connecting the plates of the condenser by
a wire or other conductor. The charge is only a surface aspect of the
state of the medium, apparently a state of strain, to which the energy
belongs.
Public-domain text, read in full here on John Shaqi.
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