_C_ = 50, _d_ = 5, _D_ = 1000;
then _i_ = 2·8 × 10⁻¹³ amperes.
Since the electrometer can readily measure a current corresponding to a
movement of half a scale division per second, we see that an
electrometer can measure a current of 3 × 10⁻¹⁴ amperes, which is
considerably below the range of the most sensitive galvanometer.
The capacity of the electrometer itself must not be considered as equal
to that of the pair of quadrants and the needle when in a position of
rest. The actual capacity is very much larger than this, on account of
the motion of the charged needle. Suppose, for example, that the needle
is charged to a high negative potential, and kept at the zero position
by an external constraint. If a quantity _Q_ of positive electricity is
given to the electrometer and its connections, the whole system is
raised to a potential _V_, such that _Q_ = _CV_, where _C_ is the
capacity of the system. When however the needle is allowed to move, it
is attracted into the charged pair of quadrants. This corresponds to the
introduction of a negatively charged body between the quadrants, and in
consequence the potential of the system is lowered to _V´_. The actual
capacity _C´_ of the system when the needle moves is thus greater than
_C_, and is given by
_C´V´_ = _CV_.
Thus the capacity of the electrometer is not a constant, but depends on
the potential of the needle, _i.e._ on the sensibility of the
electrometer.
An interesting result of practical importance follows from the variation
of the capacity of the electrometer with the potential of the needle. If
the external capacity attached to the electrometer is small compared
with that of the electrometer itself, the rate of movement of the needle
for a constant current is, in some cases, independent of the
sensibility. An electrometer may be used for several days or even weeks
to give nearly equal deflections for a constant current, without
recharging the needle, although its potential has been steadily falling
during the interval. In such a case the decrease in sensibility is
nearly proportional to the decrease in capacity of the electrometer, so
that the deflection for a given current is only slightly altered. The
theory of this action has been given by J. J. Thomson[108].
=68.= The capacity of the electrometer and its connections cannot be
measured by any of the commutator methods used for the determination of
small capacities, for in such cases the needle does not move, and the
capacity measured is not that of the electrometer system when in actual
use. The value of the capacity may, however, be determined by the method
of mixtures.
Let _C_ = capacity of electrometer and connections,
_C₁_ = capacity of a standard condenser.
Public-domain text, read in full here on John Shaqi.
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