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
Some indication of the meaning of electrical quantities has been given
in Chapter IV. Difference of electric potential between two points in an
electric field was there defined as the dynamical work done in carrying
a unit of positive electricity against the forces of the field from the
point of lower to the point of higher potential. Now by the definition
of unit quantity of electricity given in electrical theory--that
quantity which, concentrated at a point at unit distance from an equal
quantity also concentrated at a point, is repelled with unit force--we
can find, by the simple experiment of hanging two pith balls (or,
better, two hollow, gilded beads of equal size) by two fine fibres of
quartz, a metre long, say, electrifying the two balls as they hang in
contact, and observing the distance at which they then hang, the
numerical magnitude in absolute units of a charge of electricity, and
apply that to finding the charge on a large spherical conductor and the
potential at points in its field also in absolute units. If m be
the mass of a ball, g gravity in cm. sec. units, d the distance in
cms. of the centres of the balls apart, and l the length in cms. of
a thread, the charge q, say, on each ball is easily found to be
√[mgd³⧸√{4^(l² - d²)}]. Thus the charge is got in absolute
centimetre-gramme-second units in terms of the mass m obtained by
ordinary weighing, and l and d obtained by easy and exact measurements.
If one of the balls be now taken away without discharging the other, and
the latter be placed in the field of a large electrified spherical
conductor, the fibre will be deflected from the vertical by the force on
the ball. Let the two centres be now on the same level. That force is
got at once from the angle of deflection (which is easily observed),
the charge on the ball, and the value of m. The electric field-intensity
is obtained by dividing the value of the force by q. The field intensity
multiplied by D, the distance apart in cms. of the centres of the ball
and the conductor, gives the potential at the centre of the ball in
C.G.S. units. Multiplication again by D gives the charge on the
conductor.
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