Page:Elementary Text-book of Physics (Anthony, 1897).djvu/300

286 force due to the charge on the conductor, or that the potential due to the electrical forces is uniform within the conductor.

253. Law of Electrical Force.—If two charged bodies be considered, of dimensions so small that they may be neglected in comparison with the distance between the bodies, the stress between the two bodies due to electrical force is proportional directly to the product of the charges which they contain, and inversely to the square of the distance between them.

If $$Q$$ and $$Q'$$ represent two similar charges, $$r$$ the distance between them, and $$k$$ a factor depending on the units in which the charges are measured, the formula expressing the repulsion between them is $$k \frac{QQ'}{r^2}\cdot$$

Coulomb used the torsion balance (§ 109) to demonstrate this law. At one end of a glass rod suspended from the torsion wire and turning in the horizontal plane is placed a gilded pith ball, and through the lid of the case containing the apparatus can be introduced a similar insulated ball, so arranged that its centre is at the same distance from the axis of rotation of the suspended system, and m the same horizontal plane, as the centre of the first ball. This second ball may be called the carrier.

To prove the law as respects quantities, the suspended ball is brought into equilibrium at the point afterwards to be occupied by the carrier ball. The carrier ball is then charged and introduced into the case. When it comes in contact with the suspended ball, it shares its charge with it and a repulsion ensues. The torsion head must then be rotated until the suspended ball is brought to some fixed point, at a distance from the carrier which is less than that which would separate the two balls in the second part of the experiment if no torsion were brought upon the wire. The repulsion is then measured in terms of the torsion of the wire. The charge on the carrier is then halved, by touching it with a third similar insulated ball, and, the charge on the suspended ball remaining the same, the repulsion between the two balls at the same distance is again observed. If the case be so large that no disturbing effect